Eyepieces for augmented reality display system

ABSTRACT

An eyepiece waveguide for an augmented reality display system. The eyepiece waveguide can include an input coupling grating (ICG) region. The ICG region can couple an input beam into the substrate of the eyepiece waveguide as a guided beam. A first combined pupil expander-extractor (CPE) grating region can be formed on or in a surface of the substrate. The first CPE grating region can receive the guided beam, create a first plurality of diffracted beams at a plurality of distributed locations, and out-couple a first plurality of output beams. The eyepiece waveguide can also include a second CPE grating region formed on or in the opposite surface of the substrate. The second CPE grating region can receive the guided beam, create a second plurality of diffracted beams at a plurality of distributed locations, and out-couple a second plurality of output beams.

INCORPORATION BY REFERENCE TO ANY PRIORITY APPLICATIONS

This application claims priority to U.S. Provisional Patent Application62/769,933, filed Nov. 20, 2018, and entitled “EYEPIECES FOR AUGMENTEDREALITY DISPLAY SYSTEM.” The foregoing application(s), and any otherapplication(s) for which a foreign or domestic priority claim isidentified in the Application Data Sheet as filed with the presentapplication, are hereby incorporated by reference under 37 CFR 1.57.

BACKGROUND Field

This disclosure relates to eyepieces for virtual reality, augmentedreality, and mixed reality systems.

Description of the Related Art

Modern computing and display technologies have facilitated thedevelopment of virtual reality, augmented reality, and mixed realitysystems. Virtual reality, or “VR,” systems create a simulatedenvironment for a user to experience. This can be done by presentingcomputer-generated image data to the user through a head-mounteddisplay. This image data creates a sensory experience which immerses theuser in the simulated environment. A virtual reality scenario typicallyinvolves presentation of only computer-generated image data rather thanalso including actual real-world image data.

Augmented reality systems generally supplement a real-world environmentwith simulated elements. For example, augmented reality, or “AR,”systems may provide a user with a view of the surrounding real-worldenvironment via a head-mounted display. However, computer-generatedimage data can also be presented on the display to enhance thereal-world environment. This computer-generated image data can includeelements which are contextually-related to the real-world environment.Such elements can include simulated text, images, objects, etc. Mixedreality, or “MR,” systems are a type of AR system which also introducesimulated objects into a real-world environment, but these objectstypically feature a greater degree of interactivity. The simulatedelements can often times be interactive in real time.

FIG. 1 depicts an example AR scene 1 where a user sees a real-world parksetting 6 featuring people, trees, buildings in the background, and aconcrete platform 20. In addition to these items, computer-generatedimage data is also presented to the user. The computer-generated imagedata can include, for example, a robot statue 10 standing upon thereal-world platform 20, and a cartoon-like avatar character 2 flying bywhich seems to be a personification of a bumblebee, even though theseelements 2, 10 are not actually present in the real-world environment.

SUMMARY

In some embodiments, an eyepiece waveguide for an augmented realitydisplay system comprises: an optically transmissive substrate having afirst surface and a second surface; an input coupling grating (ICG)region formed on or in one of the surfaces of the substrate, the ICGregion being configured to receive an input beam of light and to couplethe input beam into the substrate as a guided beam; a first combinedpupil expander-extractor (CPE) grating region formed on or in the firstsurface of the substrate, the first CPE grating region being positionedto receive the guided beam from the ICG region and to create a firstplurality of diffracted beams at a plurality of distributed locations,and to out-couple a first plurality of output beams; and a second CPEgrating region formed on or in the second surface of the substrate, thesecond CPE grating region being positioned to receive the guided beamfrom the ICG region and to create a second plurality of diffracted beamsat a plurality of distributed locations, and to out-couple a secondplurality of output beams.

In some embodiments, an eyepiece waveguide for an augmented realitydisplay system comprises: an optically transmissive substrate; an inputcoupling grating (ICG) region; a first combined pupil expander-extractor(CPE) grating region; and a second CPE grating region, wherein the ICGregion is configured receive a set of a plurality of input beams oflight, the set of input beams being associated with a set of k-vectorswhich form a field of view (FOV) shape located at the center of ak-space annulus associated with the eyepiece waveguide; wherein the ICGregion is configured to diffract the input beams so as to couple theminto the substrate as guided beams and so as to translate the FOV shapeto a first position at least partially within the k-space annulus;wherein the first CPE grating region is configured to diffract theguided beams so as to translate the FOV shape from the first position toa second position at least partially within the k-space annulus; whereinthe second CPE grating region is configured to diffract the guided beamsso as to translate the FOV shape from the first position to a thirdposition at least partially within the k-space annulus, wherein thefirst CPE grating region is configured to diffract the guided beams soas to translate the FOV shape from the third position to the center ofthe k-space annulus, and wherein the second CPE grating region isconfigured to diffract the guided beams so as to translate the FOV shapefrom the second position to the center of the k-space annulus.

In some embodiments, an eyepiece waveguide for an augmented realitydisplay system comprises: an optically transmissive substrate having afirst surface and a second surface; an input coupling grating (ICG)region formed on or in one of the surfaces of the substrate, the ICGregion being configured to receive a beam of light and to couple thebeam into the substrate in a guided propagation mode; and a firstcombined pupil expander-extractor (CPE) grating region formed on or inthe first surface of the substrate, the first CPE grating region beingpositioned to receive the beam of light from the ICG region, and thefirst CPE grating region comprising a plurality of diffractive featuresconfigured to alter the propagation direction of the beam with a firstinteraction, and to out-couple the beam from the eyepiece waveguide witha second interaction.

In some embodiments, an eyepiece waveguide for an augmented realitydisplay system comprises: an optically transmissive substrate; an inputcoupling grating (ICG) region; and a first combined pupilexpander-extractor (CPE) grating region formed on a first side of thesubstrate, wherein the ICG region is configured to receive a set of aplurality of input beams of light, the set of input beams beingassociated with a set of k-vectors which form a field of view (FOV)shape located at the center of a k-space annulus associated with theeyepiece waveguide; wherein the ICG region is configured to diffract theinput beams so as to couple them into the substrate as guided beams andso as to translate the FOV shape to a first position at least partiallywithin the k-space annulus; wherein, with a first interaction, the firstCPE grating region is configured to diffract the guided beams so as totranslate the FOV shape from the first position to second and thirdpositions at least partially within the k-space annulus; and wherein,with a second interaction, the first CPE grating region is configured todiffract the guided beams so as to translate the FOV shape from thesecond and third positions to the center of the k-space annulus.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a user's view of augmented reality (AR) through an ARdevice.

FIG. 2 illustrates an example of a wearable display system.

FIG. 3 illustrates a conventional display system for simulatingthree-dimensional image data for a user.

FIG. 4 illustrates aspects of an approach for simulatingthree-dimensional image data using multiple depth planes.

FIGS. 5A-5C illustrate relationships between radius of curvature andfocal radius.

FIG. 6 illustrates an example of a waveguide stack for outputting imageinformation to a user in an AR eyepiece.

FIGS. 7A-7B illustrate examples of exit beams outputted by a waveguide.

FIG. 8 illustrates an example of a stacked waveguide assembly in whicheach depth plane includes images formed using multiple differentcomponent colors.

FIG. 9A illustrates a cross-sectional side view of an example of a setof stacked waveguides that each includes an in-coupling optical element.

FIG. 9B illustrates a perspective view of an example of the plurality ofstacked waveguides of FIG. 9A.

FIG. 9C illustrates a top-down plan view of an example of the pluralityof stacked waveguides of FIGS. 9A and 9B.

FIG. 10 is a perspective view of an example AR eyepiece waveguide stack.

FIG. 11 is a cross-sectional view of a portion of an example eyepiecewaveguide stack with an edge seal structure for supporting eyepiecewaveguides in a stacked configuration.

FIGS. 12A and 12B illustrate top views of an eyepiece waveguide inoperation as it projects an image toward a user's eye.

FIG. 13A illustrates a k-vector which can be used to represent thepropagation direction of a light ray or a light beam.

FIG. 13B illustrates a light ray within a planar waveguide.

FIG. 13C illustrates the permissible k-vectors for light of a givenangular frequency, co, propagating in an unbounded homogenous mediumwith refractive index, n.

FIG. 13D illustrates the permissible k-vectors for light of a givenangular frequency, co, propagating in a homogenous planar waveguidemedium with refractive index, n.

FIG. 13E illustrates an annulus in k-space which corresponds tok-vectors of light waves which can be guided within a waveguide having arefractive index, n₂.

FIG. 13F shows a k-space diagram and an eyepiece waveguide whichillustrate the relationship between a k-vector and the density ofinteractions between a guided beam corresponding to that k-vector and adiffraction grating formed on or in the waveguide.

FIG. 13G illustrates a top view of a diffraction grating and some of itsassociated k-space diffraction grating vectors (G−2, G−1, G1, G2).

FIG. 13H illustrates a transverse view of the diffraction grating andits effect, in k-space, on a k-vector corresponding to anormally-incident ray or beam of light.

FIG. 13I illustrates a transverse view of the diffraction grating shownin FIG. 13G and its effect, in k-space, on a k-vector corresponding toan obliquely-incident ray or beam of light.

FIG. 13J is a k-space diagram which illustrates the field of view of animage that is projected into an AR eyepiece waveguide.

FIG. 13K is a k-space diagram which shows the translational shift, ink-space, of the FOV rectangle which is caused by an input couplinggrating (ICG) located at the entrance pupil of an eyepiece waveguide.

FIG. 14A illustrates an example eyepiece waveguide with an ICG region,an orthogonal pupil expander (OPE) region, and an exit pupil expander(EPE) region.

FIG. 14B illustrates the k-space operation of the eyepiece waveguideshown in FIG. 14A.

FIG. 14C illustrates the optical operation of the OPE region shown inFIGS. 14A and 14B.

FIG. 14D illustrates a technique for determining the sizes and shapes ofthe OPE region and the EPE region.

FIG. 15A illustrates an example embodiment of a waveguide eyepiece inwhich the OPE region is tilted and located such that its lower border isparallel to the upper border of the EPE region.

FIG. 15B includes k-space diagrams which illustrate the operation of theeyepiece waveguide shown in FIG. 15A.

FIG. 15C is another k-space diagram which illustrates the operation ofthe eyepiece waveguide shown in FIG. 15A.

FIG. 15D is a diagram of the first generation of interactions between aninput beam and the OPE region of the eyepiece waveguide embodiment shownin FIG. 15A.

FIG. 15E is a diagram of the second generation of interactions betweenan input beam and the OPE region of the eyepiece waveguide embodimentshown in FIG. 15A.

FIG. 15F is a diagram of the third generation of interactions between aninput beam and the OPE region of the eyepiece waveguide embodiment shownin FIG. 15A.

FIG. 15G is a diagram which illustrates how a single input beam from theICG region is replicated by the OPE region and redirected toward the EPEregion as a plurality of beams.

FIG. 16A illustrates an example eyepiece waveguide that has amulti-directional pupil expander (MPE) region rather than an OPE region.

FIG. 16B illustrates a portion of an example 2D grating, along with itsassociated grating vectors, which can be used in the MPE region shown inFIG. 16A.

FIG. 16C is a k-space diagram which illustrates the k-space operation ofthe MPE region of the eyepiece waveguide shown in FIG. 16A.

FIG. 16D is a k-space diagram which further illustrates the k-spaceoperation of the MPE region of the eyepiece waveguide shown in FIG. 16A.

FIG. 16E is a k-space diagram which illustrates the k-space operation ofthe eyepiece waveguide shown in FIG. 16A.

FIG. 16F is a diagram of the first generation of interactions between aninput beam and the MPE region of the eyepiece waveguide embodiment shownin FIG. 16A.

FIG. 16G is a diagram of the second generation of interactions betweenan input beam and the MPE region of the eyepiece waveguide embodimentshown in FIG. 16A.

FIG. 16H is a diagram of the third generation of interactions between aninput beam and the MPE region of the eyepiece waveguide embodiment shownin FIG. 16A.

FIG. 16I is a diagram of the fourth generation of interactions betweenan input beam and the MPE region of the eyepiece waveguide embodimentshown in FIG. 16A.

FIG. 16J is a diagram which illustrates various paths which beams mayfollow through the MPE region and ultimately to the EPE region accordingto the eyepiece waveguide embodiment shown in FIG. 16A.

FIG. 16K is a diagram which illustrates how a single input beam from theICG region is replicated by the MPE region and redirected toward the EPEregion as a plurality of beams.

FIG. 16L is a side-by-side comparison which illustrates the performanceof an eyepiece waveguide with an OPE region versus that of an eyepiecewaveguide with an MPE region.

FIG. 16M further illustrates the performance of an eyepiece waveguidewith an MPE region versus others with OPE regions.

FIG. 17A illustrates a portion of an example 2D grating, along with itsassociated grating vectors, which can be used in the MPE region of aneyepiece waveguide.

FIG. 17B is a k-space diagram which illustrates the k-space operation ofthe MPE region of an eyepiece waveguide.

FIG. 17C is a k-space diagram which illustrates the k-space operation ofan eyepiece waveguide with an MPE region.

FIG. 17D is a diagram of the first generation of interactions between aninput beam and the MPE region of an eyepiece waveguide.

FIG. 17E is a diagram of the second generation of interactions betweenan input beam and the MPE region of an eyepiece waveguide.

FIG. 17F is a diagram of the third generation of interactions between aninput beam and the MPE region of an eyepiece waveguide.

FIG. 17G is a diagram of the fourth generation of interactions betweenan input beam and the MPE region of an eyepiece waveguide.

FIG. 18A illustrates an example eyepiece waveguide with an ICG region,two orthogonal pupil expander regions, and an exit pupil expanderregion.

FIGS. 18B and 18C illustrate top views of the EPE region of the eyepiecewaveguide shown in FIG. 18A.

FIG. 19 illustrates an embodiment of an eyepiece waveguide with anexpanded field of view.

FIG. 20A illustrates an embodiment of an expanded FOV eyepiece waveguidewith an MPE region which is overlapped by an EPE region.

FIG. 20B illustrates a portion of an example 2D grating, along with itsassociated grating vectors, which can be used in the MPE region of theeyepiece waveguide in FIG. 20A.

FIG. 20C is a k-space diagram which illustrates the k-space operation ofthe ICG region of the eyepiece waveguide in FIG. 20A.

FIG. 20D is a k-space diagram which illustrates part of the k-spaceoperation of the MPE region of the eyepiece waveguide in FIG. 20A.

FIG. 20E is a k-space diagram which illustrates another part of thek-space operation of the MPE region of the eyepiece waveguide in FIG.20A.

FIG. 20F is similar to FIG. 20E, except that it shows the k-spaceoperation of the MPE region on the FOV rectangle from FIG. 20D which wastranslated to the 9 o'clock position (instead of the 3 o'clock position,as illustrated in FIG. 20E).

FIG. 20G is a k-space diagram which illustrates the k-space operation ofthe EPE region in the eyepiece waveguide in FIG. 20A.

FIG. 20H is a k-space diagram which summarizes the k-space operation ofthe eyepiece waveguide in FIG. 20A.

FIG. 20I is a diagram which illustrates how beams of light spreadthrough the eyepiece waveguide shown in FIG. 20A.

FIG. 20J illustrates how the diffractive efficiency of the MPE region inthe eyepiece waveguide in FIG. 20A can be spatially varied so as toenhance the uniformity of luminance in the waveguide.

FIG. 20K illustrates how the diffractive efficiency of the EPE region inthe eyepiece waveguide in FIG. 20A can be spatially varied so as toenhance the uniformity of luminance in the waveguide.

FIG. 20L illustrates an embodiment of the eyepiece waveguide in FIG. 20Awhich includes one or more diffractive mirrors around the peripheraledge of the waveguide.

FIG. 20M illustrates an example embodiment of eyeglasses whichincorporate one or more instances of the eyepiece waveguide in FIG. 20A.

FIG. 20N illustrates another example embodiment of eyeglasses whichincorporate one or more instances of the eyepiece waveguide in FIG. 20A.

FIG. 21A illustrates another embodiment of an eyepiece waveguide with anMPE region which is overlapped by an EPE region.

FIG. 21B is a k-space diagram which illustrates the k-space operation ofthe eyepiece waveguide in FIG. 20A on the first set of input beamscorresponding to the first sub-portion of the FOV of an input image.

FIG. 21C is a k-space diagram which illustrates the k-space operation ofthe eyepiece waveguide in FIG. 21A on the second set of input beamscorresponding to the second sub-portion of the FOV of the input image.

FIG. 21D is a k-space diagram which summarizes the k-space operation ofthe eyepiece waveguide in FIG. 21A.

FIG. 21E illustrates an example embodiment of eyeglasses whichincorporate one or more instances of the eyepiece waveguide in FIG. 21A.

FIG. 21F illustrates example FOVs corresponding to the eyeglasses inFIG. 21E.

FIG. 21G illustrates the k-space operation of another embodiment of theeyepiece waveguide shown in FIG. 21A.

FIG. 22A illustrates an embodiment of an eyepiece waveguide that canproject an FOV which is expanded in two directions.

FIG. 22B illustrates the opposite side of the eyepiece waveguide shownin FIG. 22A.

FIG. 22C illustrates the k-space operation of the ICG regions and theOPE regions in the eyepiece waveguide embodiment in FIG. 22A.

FIG. 22D illustrates the k-space operation of the MPE region in theeyepiece waveguide embodiment in FIG. 22A.

FIG. 22E illustrates the k-space operation of the EPE region in theeyepiece waveguide embodiment in FIG. 22A.

FIG. 23 illustrates an example embodiment of an eyepiece waveguidedesigned to function with an angled projector.

FIG. 24A is an edge view of an example eyepiece waveguide that has amultiple combined pupil expander-extractor (CPE) regions.

FIG. 24B illustrates the operation of the first and second CPE regionsin both physical space and in k-space according to a first type of mainpathway of light through the eyepiece waveguide.

FIG. 24C illustrates the operation of the first and second CPE regionsin both physical space and in k-space according to a second type of mainpathway of light through the eyepiece waveguide.

FIG. 24D illustrates the operation of the first and second CPE regionsin both physical space and in k-space according to both the first andsecond types of main pathways of light through the eyepiece waveguide.

FIG. 24E is a diagram of the first generation of interactions between aninput beam and the CPE regions of the eyepiece waveguide embodimentshown in FIG. 24A.

FIG. 24F is a diagram of the second generation of interactions betweenthe input beam and the CPE regions of the eyepiece waveguide embodimentshown in FIG. 24A.

FIG. 24G is a diagram of the third generation of interactions betweenthe input beam and the CPE regions of the eyepiece waveguide embodimentshown in FIG. 24A.

FIG. 24H is a diagram of the fourth generation of interactions betweenthe input beam and the CPE regions of the eyepiece waveguide embodimentshown in FIG. 24A.

FIG. 24I is a diagram of the fifth generation of interactions betweenthe input beam and the CPE regions of the eyepiece waveguide embodimentshown in FIG. 24A.

FIG. 24J illustrates, in k-space, higher-order pathways of light throughthe eyepiece waveguide shown in FIG. 24A.

FIG. 24K is a diagram which illustrates how beams of light spreadthrough the eyepiece waveguide shown in FIG. 24A.

FIG. 25A is an edge view of an example eyepiece waveguide that has asingle 2D combined pupil expander-extractor (CPE) grating region.

FIG. 25B illustrates the operation of the 2D CPE region in both physicalspace and in k-space.

FIG. 26A is an edge view of an example eyepiece waveguide that has a 2Dcombined pupil expander-extractor (CPE) grating region on each of itssides.

FIG. 26B illustrates the so-called “screen door effect” which is animage artifact that is related to the density of output beams from aneyepiece waveguide.

FIG. 26C illustrates input coupling grating re-bounce, which is aneffect that can cause light to be disadvantageously lost from aneyepiece waveguide.

FIG. 26D illustrates how the double-sided 2D CPE gratings in FIG. 26Aincrease the density of output beams from the eyepiece waveguide.

FIG. 26E illustrates the density of output beams for the eyepiecewaveguides shown in FIG. 24A (double-sided 1D CPE gratings), FIG. 25A(single-sided 2D CPE grating), and FIG. 26A (double-sided 2D CPEgratings).

FIG. 26F shows example simulated images produced by eyepiece waveguideswith 2D CPE gratings; images for both the case of the single-sidedembodiment of FIG. 25A and the double-sided embodiment of FIG. 26A areshown.

DETAILED DESCRIPTION Overview

This disclosure describes a variety of eyepiece waveguides which can beused in AR display systems to project images to a user's eye. Theeyepiece waveguides are described both in physical terms and usingk-space representations.

Example HMD Device

FIG. 2 illustrates an example wearable display system 60. The displaysystem 60 includes a display or eyepiece 70, and various mechanical andelectronic modules and systems to support the functioning of thatdisplay 70. The display 70 may be coupled to a frame 80, which iswearable by a display system user 90 and which is configured to positionthe display 70 in front of the eyes of the user 90. The display 70 maybe considered eyewear in some embodiments. In some embodiments, aspeaker 100 is coupled to the frame 80 and is positioned adjacent theear canal of the user 90. The display system may also include one ormore microphones 110 to detect sound. The microphone 110 can allow theuser to provide inputs or commands to the system 60 (e.g., the selectionof voice menu commands, natural language questions, etc.), and/or canallow audio communication with other persons (e.g., with other users ofsimilar display systems). The microphone 110 can also collect audio datafrom the user's surroundings (e.g., sounds from the user and/orenvironment). In some embodiments, the display system may also include aperipheral sensor 120 a, which may be separate from the frame 80 andattached to the body of the user 90 (e.g., on the head, torso, anextremity, etc.). The peripheral sensor 120 a may acquire datacharacterizing the physiological state of the user 90 in someembodiments.

The display 70 is operatively coupled by a communications link 130, suchas by a wired lead or wireless connectivity, to a local data processingmodule 140 which may be mounted in a variety of configurations, such asfixedly attached to the frame 80, fixedly attached to a helmet or hatworn by the user, embedded in headphones, or removably attached to theuser 90 (e.g., in a backpack-style configuration or in a belt-couplingstyle configuration). Similarly, the sensor 120 a may be operativelycoupled by communications link 120 b (e.g., a wired lead or wirelessconnectivity) to the local processor and data module 140. The localprocessing and data module 140 may include a hardware processor, as wellas digital memory, such as non-volatile memory (e.g., flash memory or ahard disk drive), both of which may be utilized to assist in theprocessing, caching, and storage of data. The data may include data 1)captured from sensors (which may be, e.g., operatively coupled to theframe 80 or otherwise attached to the user 90), such as image capturedevices (example.g., cameras), microphones, inertial measurement units,accelerometers, compasses, GPS units, radio devices, gyros, and/or othersensors disclosed herein; and/or 2) acquired and/or processed using aremote processing module 150 and/or a remote data repository 160(including data relating to virtual content), possibly for passage tothe display 70 after such processing or retrieval. The local processingand data module 140 may be operatively coupled by communication links170, 180, such as via a wired or wireless communication links, to theremote processing module 150 and the remote data repository 160 suchthat these remote modules 150, 160 are operatively coupled to each otherand available as resources to the local processing and data module 140.In some embodiments, the local processing and data module 140 mayinclude one or more of the image capture devices, microphones, inertialmeasurement units, accelerometers, compasses, GPS units, radio devices,and/or gyros. In some other embodiments, one or more of these sensorsmay be attached to the frame 80, or may be standalone devices thatcommunicate with the local processing and data module 140 by wired orwireless communication pathways.

The remote processing module 150 may include one or more processors toanalyze and process data, such as image and audio information. In someembodiments, the remote data repository 160 may be a digital datastorage facility, which may be available through the internet or othernetworking configuration in a “cloud” resource configuration. In someembodiments, the remote data repository 160 may include one or moreremote servers, which provide information (e.g., information forgenerating augmented reality content) to the local processing and datamodule 140 and/or the remote processing module 150. In otherembodiments, all data is stored and all computations are performed inthe local processing and data module, allowing fully autonomous use froma remote module.

The perception of an image as being “three-dimensional” or “3-D” may beachieved by providing slightly different presentations of the image toeach eye of the user. FIG. 3 illustrates a conventional display systemfor simulating three-dimensional image data for a user. Two distinctimages 190, 200—one for each eye 210, 220—are output to the user. Theimages 190, 200 are spaced from the eyes 210, 220 by a distance 230along an optical or z-axis that is parallel to the line of sight of theuser. The images 190, 200 are flat and the eyes 210, 220 may focus onthe images by assuming a single accommodated state. Such 3-D displaysystems rely on the human visual system to combine the images 190, 200to provide a perception of depth and/or scale for the combined image.

However, the human visual system is complicated and providing arealistic perception of depth is challenging. For example, many users ofconventional “3-D” display systems find such systems to be uncomfortableor may not perceive a sense of depth at all. Objects may be perceived asbeing “three-dimensional” due to a combination of vergence andaccommodation. Vergence movements (e.g., rotation of the eyes so thatthe pupils move toward or away from each other to converge therespective lines of sight of the eyes to fixate upon an object) of thetwo eyes relative to each other are closely associated with focusing (or“accommodation”) of the lenses of the eyes. Under normal conditions,changing the focus of the lenses of the eyes, or accommodating the eyes,to change focus from one object to another object at a differentdistance will automatically cause a matching change in vergence to thesame distance, under a relationship known as the “accommodation-vergencereflex,” as well as pupil dilation or constriction. Likewise, undernormal conditions, a change in vergence will trigger a matching changein accommodation of lens shape and pupil size. As noted herein, manystereoscopic or “3-D” display systems display a scene using slightlydifferent presentations (and, so, slightly different images) to each eyesuch that a three-dimensional perspective is perceived by the humanvisual system. Such systems can be uncomfortable for some users,however, since they simply provide image information at a singleaccommodated state and work against the “accommodation-vergence reflex.”Display systems that provide a better match between accommodation andvergence may form more realistic and comfortable simulations ofthree-dimensional image data.

FIG. 4 illustrates aspects of an approach for simulatingthree-dimensional image data using multiple depth planes. With referenceto FIG. 4, the eyes 210, 220 assume different accommodated states tofocus on objects at various distances on the z-axis. Consequently, aparticular accommodated state may be said to be associated with aparticular one of the illustrated depth planes 240, which has anassociated focal distance, such that objects or parts of objects in aparticular depth plane are in focus when the eye is in the accommodatedstate for that depth plane. In some embodiments, three-dimensional imagedata may be simulated by providing different presentations of an imagefor each of the eyes 210, 220, and also by providing differentpresentations of the image corresponding to multiple depth planes. Whilethe respective fields of view of the eyes 210, 220 are shown as beingseparate for clarity of illustration, they may overlap, for example, asdistance along the z-axis increases. In addition, while the depth planesare shown as being flat for ease of illustration, it will be appreciatedthat the contours of a depth plane may be curved in physical space, suchthat all features in a depth plane are in focus with the eye in aparticular accommodated state.

The distance between an object and an eye 210 or 220 may also change theamount of divergence of light from that object, as viewed by that eye.FIGS. 5A-5C illustrate relationships between distance and the divergenceof light rays. The distance between the object and the eye 210 isrepresented by, in order of decreasing distance, R1, R2, and R3. Asshown in FIGS. 5A-5C, the light rays become more divergent as distanceto the object decreases. As distance increases, the light rays becomemore collimated. Stated another way, it may be said that the light fieldproduced by a point (the object or a part of the object) has a sphericalwavefront curvature, which is a function of how far away the point isfrom the eye of the user. The curvature increases with decreasingdistance between the object and the eye 210. Consequently, at differentdepth planes, the degree of divergence of light rays is also different,with the degree of divergence increasing with decreasing distancebetween depth planes and the user's eye 210. While only a single eye 210is illustrated for clarity of illustration in FIGS. 5A-5C and otherfigures herein, it will be appreciated that the discussions regardingthe eye 210 may be applied to both eyes 210 and 220 of a user.

A highly believable simulation of perceived depth may be achieved byproviding, to the eye, different presentations of an image correspondingto each of a limited number of depth planes. The different presentationsmay be separately focused by the user's eye, thereby helping to providethe user with depth cues based on the amount of accommodation of the eyerequired to bring into focus different image features for the scenelocated on different depth planes and/or based on observing differentimage features on different depth planes being out of focus.

Example of a Waveguide Stack Assembly for an AR or MR Eyepiece

FIG. 6 illustrates an example of a waveguide stack for outputting imageinformation to a user in an AR eyepiece. A display system 250 includes astack of waveguides, or stacked waveguide assembly, 260 that may beutilized to provide three-dimensional perception to the eye/brain usinga plurality of waveguides 270, 280, 290, 300, 310. In some embodiments,the display system 250 is the system 60 of FIG. 2, with FIG. 6schematically showing some parts of that system 60 in greater detail.For example, the waveguide assembly 260 may be part of the display 70 ofFIG. 2. It will be appreciated that the display system 250 may beconsidered a light field display in some embodiments.

The waveguide assembly 260 may also include a plurality of features 320,330, 340, 350 between the waveguides. In some embodiments, the features320, 330, 340, 350 may be one or more lenses. The waveguides 270, 280,290, 300, 310 and/or the plurality of lenses 320, 330, 340, 350 may beconfigured to send image information to the eye with various levels ofwavefront curvature or light ray divergence. Each waveguide level may beassociated with a particular depth plane and may be configured to outputimage information corresponding to that depth plane. Image injectiondevices 360, 370, 380, 390, 400 may function as a source of light forthe waveguides and may be utilized to inject image information into thewaveguides 270, 280, 290, 300, 310, each of which may be configured, asdescribed herein, to distribute incoming light across each respectivewaveguide, for output toward the eye 210. Light exits an output surface410, 420, 430, 440, 450 of each respective image injection device 360,370, 380, 390, 400 and is injected into a corresponding input surface460, 470, 480, 490, 500 of the respective waveguides 270, 280, 290, 300,310. In some embodiments, the each of the input surfaces 460, 470, 480,490, 500 may be an edge of a corresponding waveguide, or may be part ofa major surface of the corresponding waveguide (that is, one of thewaveguide surfaces directly facing the world 510 or the user's eye 210).In some embodiments, a beam of light (e.g. a collimated beam) may beinjected into each waveguide and may be replicated, such as by samplinginto beamlets by diffraction, in the waveguide and then directed towardthe eye 210 with an amount of optical power corresponding to the depthplane associated with that particular waveguide. In some embodiments, asingle one of the image injection devices 360, 370, 380, 390, 400 may beassociated with, and inject light into, a plurality (e.g., three) of thewaveguides 270, 280, 290, 300, 310.

In some embodiments, the image injection devices 360, 370, 380, 390, 400are discrete displays that each produce image information for injectioninto a corresponding waveguide 270, 280, 290, 300, 310, respectively. Insome other embodiments, the image injection devices 360, 370, 380, 390,400 are the output ends of a single multiplexed display which maytransmit image information via one or more optical conduits (such asfiber optic cables) to each of the image injection devices 360, 370,380, 390, 400. It will be appreciated that the image informationprovided by the image injection devices 360, 370, 380, 390, 400 mayinclude light of different wavelengths, or colors.

In some embodiments, the light injected into the waveguides 270, 280,290, 300, 310 is provided by a light projector system 520, whichincludes a light module 530, which may include a light source or lightemitter, such as a light emitting diode (LED). The light from the lightmodule 530 may be directed to, and modulated by, a light modulator 540(e.g., a spatial light modulator), via a beamsplitter (BS) 550. Thelight modulator 540 may spatially and/or temporally change the perceivedintensity of the light injected into the waveguides 270, 280, 290, 300,310. Examples of spatial light modulators include liquid crystaldisplays (LCD), including a liquid crystal on silicon (LCOS) displays,and digital light processing (DLP) displays.

In some embodiments, the light projector system 520, or one or morecomponents thereof, may be attached to the frame 80 (FIG. 2). Forexample, the light projector system 520 may be part of a temporalportion (e.g., ear stem 82) of the frame 80 or disposed at an edge ofthe display 70. In some embodiments, the light module 530 may beseparate from the BS 550 and/or light modulator 540.

In some embodiments, the display system 250 may be a scanning fiberdisplay comprising one or more scanning fibers to project light invarious patterns (e.g., raster scan, spiral scan, Lissajous patterns,etc.) into one or more waveguides 270, 280, 290, 300, 310 and ultimatelyinto the eye 210 of the user. In some embodiments, the illustrated imageinjection devices 360, 370, 380, 390, 400 may schematically represent asingle scanning fiber or a bundle of scanning fibers configured toinject light into one or a plurality of the waveguides 270, 280, 290,300, 310. In some other embodiments, the illustrated image injectiondevices 360, 370, 380, 390, 400 may schematically represent a pluralityof scanning fibers or a plurality of bundles of scanning fibers, each ofwhich are configured to inject light into an associated one of thewaveguides 270, 280, 290, 300, 310. One or more optical fibers maytransmit light from the light module 530 to the one or more waveguides270, 280, 290, 300, and 310. In addition, one or more interveningoptical structures may be provided between the scanning fiber, orfibers, and the one or more waveguides 270, 280, 290, 300, 310 to, forexample, redirect light exiting the scanning fiber into the one or morewaveguides 270, 280, 290, 300, 310.

A controller 560 controls the operation of the stacked waveguideassembly 260, including operation of the image injection devices 360,370, 380, 390, 400, the light source 530, and the light modulator 540.In some embodiments, the controller 560 is part of the local dataprocessing module 140. The controller 560 includes programming (e.g.,instructions in a non-transitory medium) that regulates the timing andprovision of image information to the waveguides 270, 280, 290, 300,310. In some embodiments, the controller may be a single integraldevice, or a distributed system connected by wired or wirelesscommunication channels. The controller 560 may be part of the processingmodules 140 or 150 (FIG. 2) in some embodiments.

The waveguides 270, 280, 290, 300, 310 may be configured to propagatelight within each respective waveguide by total internal reflection(TIR). The waveguides 270, 280, 290, 300, 310 may each be planar or haveanother shape (e.g., curved), with major top and bottom surfaces andedges extending between those major top and bottom surfaces. In theillustrated configuration, the waveguides 270, 280, 290, 300, 310 mayeach include out-coupling optical elements 570, 580, 590, 600, 610 thatare configured to extract light out of a waveguide by redirecting thelight, propagating within each respective waveguide, out of thewaveguide to output image information to the eye 210. Extracted lightmay also be referred to as out-coupled light and the out-couplingoptical elements light may also be referred to light extracting opticalelements. An extracted beam of light may be output by the waveguide atlocations at which the light propagating in the waveguide strikes alight extracting optical element. The out-coupling optical elements 570,580, 590, 600, 610 may be, for example, diffractive optical features,including diffractive gratings, as discussed further herein. While theout-coupling optical elements 570, 580, 590, 600, 610 are illustrated asbeing disposed at the bottom major surfaces of the waveguides 270, 280,290, 300, 310, in some embodiments they may be disposed at the topand/or bottom major surfaces, and/or may be disposed directly in thevolume of the waveguides 270, 280, 290, 300, 310, as discussed furtherherein. In some embodiments, the out-coupling optical elements 570, 580,590, 600, 610 may be formed in a layer of material that is attached to atransparent substrate to form the waveguides 270, 280, 290, 300, 310. Insome other embodiments, the waveguides 270, 280, 290, 300, 310 may be amonolithic piece of material and the out-coupling optical elements 570,580, 590, 600, 610 may be formed on a surface and/or in the interior ofthat piece of material.

Each waveguide 270, 280, 290, 300, 310 may output light to form an imagecorresponding to a particular depth plane. For example, the waveguide270 nearest the eye may deliver collimated beams of light to the eye210. The collimated beams of light may be representative of the opticalinfinity focal plane. The next waveguide up 280 may output collimatedbeams of light which pass through the first lens 350 (e.g., a negativelens) before reaching the eye 210. The first lens 350 may add a slightconvex wavefront curvature to the collimated beams so that the eye/braininterprets light coming from that waveguide 280 as originating from afirst focal plane closer inward toward the eye 210 from opticalinfinity. Similarly, the third waveguide 290 passes its output lightthrough both the first lens 350 and the second lens 340 before reachingthe eye 210. The combined optical power of the first lens 350 and thesecond lens 340 may add another incremental amount of wavefrontcurvature so that the eye/brain interprets light coming from the thirdwaveguide 290 as originating from a second focal plane that is evencloser inward from optical infinity than was light from the secondwaveguide 280.

The other waveguide layers 300, 310 and lenses 330, 320 are similarlyconfigured, with the highest waveguide 310 in the stack sending itsoutput through all of the lenses between it and the eye for an aggregatefocal power representative of the closest focal plane to the person. Tocompensate for the stack of lenses 320, 330, 340, 350 whenviewing/interpreting light coming from the world 510 on the other sideof the stacked waveguide assembly 260, a compensating lens layer 620 maybe disposed at the top of the stack to compensate for the aggregateoptical power of the lens stack 320, 330, 340, 350 below. Such aconfiguration provides as many perceived focal planes as there areavailable waveguide/lens pairings. Both the out-coupling opticalelements of the waveguides and the focusing aspects of the lenses may bestatic (i.e., not dynamic or electro-active). In some alternativeembodiments, either or both may be dynamic using electro-activefeatures.

In some embodiments, two or more of the waveguides 270, 280, 290, 300,310 may have the same associated depth plane. For example, multiplewaveguides 270, 280, 290, 300, 310 may output images set to the samedepth plane, or multiple subsets of the waveguides 270, 280, 290, 300,310 may output images set to the same plurality of depth planes, withone set for each depth plane. This can provide advantages for forming atiled image to provide an expanded field of view at those depth planes.

The out-coupling optical elements 570, 580, 590, 600, 610 may beconfigured to both redirect light out of their respective waveguides andto output this light with the appropriate amount of divergence orcollimation for a particular depth plane associated with the waveguide.As a result, waveguides having different associated depth planes mayhave different configurations of out-coupling optical elements 570, 580,590, 600, 610, which output light with a different amount of divergencedepending on the associated depth plane. In some embodiments, the lightextracting optical elements 570, 580, 590, 600, 610 may be volumetric orsurface features, which may be configured to output light at specificangles. For example, the light extracting optical elements 570, 580,590, 600, 610 may be volume holograms, surface holograms, and/ordiffraction gratings. In some embodiments, the features 320, 330, 340,350 may not be lenses; rather, they may simply be spacers (e.g.,cladding layers and/or structures for forming air gaps).

In some embodiments, the out-coupling optical elements 570, 580, 590,600, 610 are diffractive features with a diffractive efficiencysufficiently low such that only a portion of the power of the light in abeam is re-directed toward the eye 210 with each interaction, while therest continues to move through a waveguide via TIR. Accordingly, theexit pupil of the light module 530 is replicated across the waveguide tocreate a plurality of output beams carrying the image information fromlight source 530, effectively expanding the number of locations wherethe eye 210 may intercept the replicated light source exit pupil. Thesediffractive features may also have a variable diffractive efficiencyacross their geometry to improve uniformity of light output by thewaveguide.

In some embodiments, one or more diffractive features may be switchablebetween “on” states in which they actively diffract, and “off” states inwhich they do not significantly diffract. For instance, a switchablediffractive element may include a layer of polymer dispersed liquidcrystal in which microdroplets form a diffraction pattern in a hostmedium, and the refractive index of the microdroplets may be switched tosubstantially match the refractive index of the host material (in whichcase the pattern does not appreciably diffract incident light) or themicrodroplet may be switched to an index that does not match that of thehost medium (in which case the pattern actively diffracts incidentlight).

In some embodiments, a camera assembly 630 (e.g., a digital camera,including visible light and IR light cameras) may be provided to captureimages of the eye 210, parts of the eye 210, or at least a portion ofthe tissue surrounding the eye 210 to, for example, detect user inputs,extract biometric information from the eye, estimate and track the gazedirection of the eye, to monitor the physiological state of the user,etc. In some embodiments, the camera assembly 630 may include an imagecapture device and a light source to project light (e.g., IR or near-IRlight) to the eye, which may then be reflected by the eye and detectedby the image capture device. In some embodiments, the light sourceincludes light emitting diodes (“LEDs”), emitting in IR or near-IR. Insome embodiments, the camera assembly 630 may be attached to the frame80 (FIG. 2) and may be in electrical communication with the processingmodules 140 or 150, which may process image information from the cameraassembly 630 to make various determinations regarding, for example, thephysiological state of the user, the gaze direction of the wearer, irisidentification, etc. In some embodiments, one camera assembly 630 may beutilized for each eye, to separately monitor each eye.

FIG. 7A illustrates an example of exit beams output by a waveguide. Onewaveguide is illustrated (with a perspective view), but other waveguidesin the waveguide assembly 260 (FIG. 6) may function similarly. Light 640is injected into the waveguide 270 at the input surface 460 of thewaveguide 270 and propagates within the waveguide 270 by TIR. Throughinteraction with diffractive features, light exits the waveguide as exitbeams 650. The exit beams 650 replicate the exit pupil from a projectordevice which projects images into the waveguide. Any one of the exitbeams 650 includes a sub-portion of the total energy of the input light640. And in a perfectly efficient system, the summation of the energy inall the exit beams 650 would equal the energy of the input light 640.The exit beams 650 are illustrated as being substantially parallel inFIG. 7A but, as discussed herein, some amount of optical power may beimparted depending on the depth plane associated with the waveguide 270.Parallel exit beams may be indicative of a waveguide with out-couplingoptical elements that out-couple light to form images that appear to beset on a depth plane at a large distance (e.g., optical infinity) fromthe eye 210. Other waveguides or other sets of out-coupling opticalelements may output an exit beam pattern that is more divergent, asshown in FIG. 7B, which would require the eye 210 to accommodate to acloser distance to bring it into focus on the retina and would beinterpreted by the brain as light from a distance closer to the eye 210than optical infinity.

In some embodiments, a full color image may be formed at each depthplane by overlaying images in each of the component colors (e.g., threeor more component colors, such as red, green, and blue). FIG. 8illustrates an example of a stacked waveguide assembly in which eachdepth plane includes images formed using multiple different componentcolors. The illustrated embodiment shows depth planes 240 a-240 f,although more or fewer depths are also contemplated. Each depth planemay have three or more component color images associated with it,including: a first image of a first color, G; a second image of a secondcolor, R; and a third image of a third color, B. Different depth planesare indicated in the figure by different diopter powers following theletters G, R, and B. The numbers following each of these lettersindicate diopters (1/m), or inverse distance of the depth plane from auser, and each box in the figure represents an individual componentcolor image. In some embodiments, to account for differences in theeye's focusing of light of different wavelengths, the exact placement ofthe depth planes for different component colors may vary. For example,different component color images for a given depth plane may be placedon depth planes corresponding to different distances from the user. Suchan arrangement may increase visual acuity and user comfort or maydecrease chromatic aberrations.

In some embodiments, light of each component color may be output by asingle dedicated waveguide and, consequently, each depth plane may havemultiple waveguides associated with it. In such embodiments, each box inthe figure may be understood to represent an individual waveguide, andthree waveguides may be provided per depth plane so as to display threecomponent color images per depth plane. While the waveguides associatedwith each depth plane are shown adjacent to one another in this drawingfor ease of illustration, it will be appreciated that, in a physicaldevice, the waveguides may all be arranged in a stack with one waveguideper level. In some other embodiments, multiple component colors may beoutput by the same waveguide, such that, for example, only a singlewaveguide may be provided per depth plane.

With continued reference to FIG. 8, in some embodiments, G is the colorgreen, R is the color red, and B is the color blue. In some otherembodiments, other colors associated with other wavelengths of light,including yellow, magenta and cyan, may be used in addition to or mayreplace one or more of red, green, or blue. In some embodiments,features 320, 330, 340, and 350 may be active or passive optical filtersconfigured to block or selectively pass light from the ambientenvironment to the user's eyes.

References to a given color of light throughout this disclosure shouldbe understood to encompass light of one or more wavelengths within arange of wavelengths of light that are perceived by a user as being ofthat given color. For example, red light may include light of one ormore wavelengths in the range of about 620-780 nm, green light mayinclude light of one or more wavelengths in the range of about 492-577nm, and blue light may include light of one or more wavelengths in therange of about 435-493 nm.

In some embodiments, the light source 530 (FIG. 6) may be configured toemit light of one or more wavelengths outside the visual perceptionrange of the user, for example, IR or ultraviolet wavelengths. IR lightcan include light with wavelengths in a range from 700 nm to 10 μm. Insome embodiments, IR light can include near-IR light with wavelengths ina range from 700 nm to 1.5 μm. In addition, the in-coupling,out-coupling, and other light redirecting structures of the waveguidesof the display 250 may be configured to direct and emit this light outof the display towards the user's eye 210, e.g., for imaging or userstimulation applications.

With reference now to FIG. 9A, in some embodiments, light impinging on awaveguide may need to be redirected so as to in-couple the light intothe waveguide. An in-coupling optical element may be used to redirectand in-couple the light into its corresponding waveguide. FIG. 9Aillustrates a cross-sectional side view of an example of a set 660 ofstacked waveguides that each includes an in-coupling optical element.The waveguides may each be configured to output light of one or moredifferent wavelengths, or one or more different ranges of wavelengths.It will be appreciated that the stack 660 may correspond to the stack260 (FIG. 6) and the illustrated waveguides of the stack 660 maycorrespond to part of the plurality of waveguides 270, 280, 290, 300,310, except that light from one or more of the image injection devices360, 370, 380, 390, 400 is injected into the waveguides from a positionor orientation that requires light to be redirected for in-coupling.

The illustrated set 660 of stacked waveguides includes waveguides 670,680, and 690. Each waveguide includes an associated in-coupling opticalelement (which may also be referred to as a light input area on thewaveguide), with, for example, in-coupling optical element 700 disposedon a major surface (e.g., an upper major surface) of waveguide 670,in-coupling optical element 710 disposed on a major surface (e.g., anupper major surface) of waveguide 680, and in-coupling optical element720 disposed on a major surface (e.g., an upper major surface) ofwaveguide 690. In some embodiments, one or more of the in-couplingoptical elements 700, 710, 720 may be disposed on the bottom majorsurface of the respective waveguide 670, 680, 690 (particularly wherethe one or more in-coupling optical elements are reflective opticalelements). As illustrated, the in-coupling optical elements 700, 710,720 may be disposed on the upper major surface of their respectivewaveguide 670, 680, 690 (or the top of the next lower waveguide),particularly where those in-coupling optical elements are transmissiveoptical elements. In some embodiments, the in-coupling optical elements700, 710, 720 may be disposed in the body of the respective waveguide670, 680, 690. In some embodiments, as discussed herein, the in-couplingoptical elements 700, 710, 720 are wavelength selective, such that theyselectively redirect one or more wavelengths of light, whiletransmitting other wavelengths of light. While illustrated on one sideor corner of their respective waveguide 670, 680, 690, it will beappreciated that the in-coupling optical elements 700, 710, 720 may bedisposed in other areas of their respective waveguide 670, 680, 690 insome embodiments.

As illustrated, the in-coupling optical elements 700, 710, 720 may belaterally offset from one another. In some embodiments, each in-couplingoptical element may be offset such that it receives light without thatlight passing through another in-coupling optical element. For example,each in-coupling optical element 700, 710, 720 may be configured toreceive light from a different image injection device 360, 370, 380,390, and 400 as shown in FIG. 6, and may be separated (e.g., laterallyspaced apart) from other in-coupling optical elements 700, 710, 720 suchthat it substantially does not receive light from the other ones of thein-coupling optical elements 700, 710, 720.

Each waveguide also includes associated light distributing elements,with, for example, light distributing elements 730 disposed on a majorsurface (e.g., a top major surface) of waveguide 670, light distributingelements 740 disposed on a major surface (e.g., a top major surface) ofwaveguide 680, and light distributing elements 750 disposed on a majorsurface (e.g., a top major surface) of waveguide 690. In some otherembodiments, the light distributing elements 730, 740, 750 may bedisposed on a bottom major surface of associated waveguides 670, 680,690, respectively. In some other embodiments, the light distributingelements 730, 740, 750 may be disposed on both top and bottom majorsurface of associated waveguides 670, 680, 690 respectively; or thelight distributing elements 730, 740, 750, may be disposed on differentones of the top and bottom major surfaces in different associatedwaveguides 670, 680, 690, respectively.

The waveguides 670, 680, 690 may be spaced apart and separated by, forexample, gas, liquid, or solid layers of material. For example, asillustrated, layer 760 a may separate waveguides 670 and 680; and layer760 b may separate waveguides 680 and 690. In some embodiments, thelayers 760 a and 760 b are formed of low refractive index materials(that is, materials having a lower refractive index than the materialforming the immediately adjacent one of waveguides 670, 680, 690).Preferably, the refractive index of the material forming the layers 760a, 760 b is at least 0.05, or at least 0.10, less than the refractiveindex of the material forming the waveguides 670, 680, 690.Advantageously, the lower refractive index layers 760 a, 760 b mayfunction as cladding layers that facilitate TIR of light through thewaveguides 670, 680, 690 (e.g., TIR between the top and bottom majorsurfaces of each waveguide). In some embodiments, the layers 760 a, 760b are formed of air. While not illustrated, it will be appreciated thatthe top and bottom of the illustrated set 660 of waveguides may includeimmediately neighboring cladding layers.

Preferably, for ease of manufacturing and other considerations, thematerial forming the waveguides 670, 680, 690 are similar or the same,and the material forming the layers 760 a, 760 b are similar or thesame. In other embodiments, the material forming the waveguides 670,680, 690 may be different between one or more waveguides, or thematerial forming the layers 760 a, 760 b may be different, while stillholding to the various refractive index relationships noted above.

With continued reference to FIG. 9A, light rays 770, 780, 790 areincident on the set 660 of waveguides. Light rays 770, 780, 790 may beinjected into the waveguides 670, 680, 690 by one or more imageinjection devices 360, 370, 380, 390, 400 (FIG. 6).

In some embodiments, the light rays 770, 780, 790 have differentproperties (e.g., different wavelengths or different ranges ofwavelengths), which may correspond to different colors. The in-couplingoptical elements 700, 710, 720 each re-direct the incident light suchthat the light propagates through a respective one of the waveguides670, 680, 690 by TIR.

For example, in-coupling optical element 700 may be configured tore-direct ray 770, which has a first wavelength or range of wavelengths.Similarly, transmitted ray 780 impinges on and is re-directed byin-coupling optical element 710, which is configured to re-direct lightof a second wavelength or range of wavelengths. Likewise, ray 790 isre-directed by in-coupling optical element 720, which is configured toselectively re-direct light of third wavelength or range of wavelengths.

With continued reference to FIG. 9A, light rays 770, 780, 790 arere-directed so that they propagate through a corresponding waveguide670, 680, 690; that is, the in-coupling optical element 700, 710, 720 ofeach waveguide re-directs light into that corresponding waveguide 670,680, 690 to in-couple light into that corresponding waveguide. The lightrays 770, 780, 790 are re-directed at angles that cause the light topropagate through the respective waveguide 670, 680, 690 by TIR. Thelight rays 770, 780, 790 propagate through the respective waveguide 670,680, 690 by TIR until interacting with the waveguide's correspondinglight distributing elements 730, 740, 750.

With reference now to FIG. 9B, a perspective view of an example of theplurality of stacked waveguides of FIG. 9A is illustrated. As notedabove, the light rays 770, 780, 790, are in-coupled by the in-couplingoptical elements 700, 710, 720, respectively, and then propagate by TIRwithin the waveguides 670, 680, 690, respectively. The light rays 770,780, 790 then interact with the light distributing elements 730, 740,750, respectively. The light distributing elements 730, 740, 750re-direct the light rays 770, 780, 790 so that they propagate towardsthe out-coupling optical elements 800, 810, and 820, respectively.

In some embodiments, the light distributing elements 730, 740, 750 areorthogonal pupil expanders (OPEs). In some embodiments, the OPEs bothre-direct light to the out-coupling optical elements 800, 810, 820 andalso expand the pupil associated with this light by sampling the lightrays 770, 780, 790 at many locations across the light distributingelements 730, 740, 750 as they propagate to the out-coupling opticalelements. In some embodiments (e.g., where the exit pupil is already ofa desired size), the light distributing elements 730, 740, 750 may beomitted and the in-coupling optical elements 700, 710, 720 may beconfigured to re-direct light directly to the out-coupling opticalelements 800, 810, 820. For example, with reference to FIG. 9A, thelight distributing elements 730, 740, 750 may be replaced without-coupling optical elements 800, 810, 820, respectively. In someembodiments, the out-coupling optical elements 800, 810, 820 are exitpupils (EPs) or exit pupil expanders (EPEs) that re-direct light out ofthe waveguides and toward a user's eye 210 (FIG. 7). The OPEs may beconfigured to increase the dimensions of the eye box in at least oneaxis and the EPEs may be configured to increase the eye box in an axiscrossing (e.g., orthogonal to) the axis of the OPEs.

Accordingly, with reference to FIGS. 9A and 9B, in some embodiments, theset 660 of waveguides includes waveguides 670, 680, 690; in-couplingoptical elements 700, 710, 720; light distributing elements (e.g., OPEs)730, 740, 750; and out-coupling optical elements (e.g., EPEs) 800, 810,820 for each component color. The waveguides 670, 680, 690 may bestacked with an air gap/cladding layer between each one. The in-couplingoptical elements 700, 710, 720 direct incident light (with differentin-coupling optical elements receiving light of different wavelengths)into a corresponding waveguide. The light then propagates at angleswhich support TIR within the respective waveguide 670, 680, 690. SinceTIR only occurs for a certain range of angles, the range of propagationangles of the light rays 770, 780, 790 is limited. The range of angleswhich support TIR may be thought of in such an example as the angularlimits of the field of view which can be displayed by the waveguides670, 680, 690. In the example shown, light ray 770 (e.g., blue light) isin-coupled by the first in-coupling optical element 700, and thencontinues to reflect back and forth from the surfaces of the waveguidewhile traveling down the waveguide, with the light distributing element(e.g., OPE) 730 progressively sampling it to create additionalreplicated rays which are directed toward the out-coupling opticalelement (e.g., EPE) 800, in a manner described earlier. The light rays780 and 790 (e.g., green and red light, respectively) will pass throughthe waveguide 670, with light ray 780 impinging on and being in-coupledby in-coupling optical element 710. The light ray 780 then propagatesdown the waveguide 680 via TIR, proceeding on to its light distributingelement (e.g., OPE) 740 and then the out-coupling optical element (e.g.,EPE) 810. Finally, light ray 790 (e.g., red light) passes through thewaveguides 670, 680 to impinge on the light in-coupling optical element720 of the waveguide 690. The light in-coupling optical element 720in-couples the light ray 790 such that the light ray propagates to lightdistributing element (e.g., OPE) 750 by TIR, and then to theout-coupling optical element (e.g., EPE) 820 by TIR. The out-couplingoptical element 820 then finally out-couples the light ray 790 to theuser, who also receives the out-coupled light from the other waveguides670, 680.

FIG. 9C illustrates a top-down plan view of an example of the pluralityof stacked waveguides of FIGS. 9A and 9B. As illustrated, the waveguides670, 680, 690, along with each waveguide's associated light distributingelement 730, 740, 750 and associated out-coupling optical element 800,810, 820, may be vertically aligned. However, as discussed herein, thein-coupling optical elements 700, 710, 720 are not vertically aligned;rather, the in-coupling optical elements may be non-overlapping (e.g.,laterally spaced apart as seen in the top-down view). Thisnon-overlapping spatial arrangement may facilitate the injection oflight from different sources into different waveguides on a one-to-onebasis, thereby allowing a specific light source to be uniquely opticallycoupled to a specific waveguide. In some embodiments, arrangementsincluding non-overlapping spatially separated in-coupling opticalelements may be referred to as a shifted pupil system, and thein-coupling optical elements within these arrangements may correspond tosub pupils.

FIG. 10 is a perspective view of an example AR eyepiece waveguide stack1000. The eyepiece waveguide stack 1000 may include a world-side coverwindow 1002 and an eye-side cover window 1006 to protect one or moreeyepiece waveguides 1004 positioned between the cover windows. In otherembodiments, one or both of the cover windows 1002, 1006 may be omitted.As already discussed, the eyepiece waveguides 1004 may be arranged in alayered configuration. The eyepiece waveguides 1004 may be coupledtogether, for instance, with each individual eyepiece waveguide beingcoupled to one or more adjacent eyepiece waveguides. In someembodiments, the waveguides 1004 may be coupled together with an edgeseal (such as the edge seal 1108 shown in FIG. 11) such that adjacenteyepiece waveguides 1004 are not in direct contact with each other.

Each of the eyepiece waveguides 1004 can be made of a substrate materialthat is at least partially transparent, such as glass, plastic,polycarbonate, sapphire, etc. The selected material may have an index ofrefraction above 1.4, for example, or above 1.6, or above 1.8, tofacilitate light guiding. The thickness of each eyepiece waveguidesubstrate may be, for example, 325 microns or less, though otherthicknesses can also be used. Each eyepiece waveguide can include one ormore in-coupling regions, light distributing regions, image expandingregions, and out-coupling regions, which may be made up of diffractivefeatures formed on or in each waveguide substrate 902.

Although not illustrated in FIG. 10, the eyepiece waveguide stack 1000can include a physical support structure for supporting it in front of auser's eyes. In some embodiments, the eyepiece waveguide stack 1000 ispart of a head-mounted display system 60, as illustrated in FIG. 2. Ingeneral, the eyepiece waveguide stack 1000 is supported such that anout-coupling region is directly in front of a user's eye. It should beunderstood that FIG. 10 illustrates only the portion of the eyepiecewaveguide stack 1000 which corresponds to one of the user's eyes. Acomplete eyepiece may include a mirror image of the same structure, withthe two halves possibly separated by a nose piece.

In some embodiments, the eyepiece waveguide stack 1000 can project colorimage data from multiple depth planes into the user's eyes. The imagedata displayed by each individual eyepiece waveguide 1004 in theeyepiece 1000 may correspond to a selected color component of the imagedata for a selected depth plane. For example, since the eyepiecewaveguide stack 1000 includes six eyepiece waveguides 1004, it canproject color image data (e.g., made up of red, green, and bluecomponents) corresponding to two different depth planes: one eyepiecewaveguide 1004 per color component per depth plane. Other embodimentscan include eyepiece waveguides 1004 for more or fewer color componentsand/or more or fewer depth planes.

FIG. 11 is a cross-sectional view of a portion of an example eyepiecewaveguide stack 1100 with an edge seal structure 1108 for supportingeyepiece waveguides 1104 in a stacked configuration. The edge sealstructure 1108 aligns the eyepiece waveguides 1104 and separates themfrom one another with air space or another material disposed between.Although not illustrated, the edge seal structure 1108 can extend aroundthe entire perimeter of the stacked waveguide configuration. In FIG. 11,the separation between each eyepiece waveguide is 0.027 mm, though otherdistances are also possible.

In the illustrated embodiment, there are two eyepiece waveguides 1104designed to display red image data, one for a 3 m depth plane and theother for a 1 m depth plane. (Again, the divergence of the beams oflight output by an eyepiece waveguide 1104 can make the image dataappear to originate from a depth plane located at a particulardistance.) Similarly, there are two eyepiece waveguides 1104 designed todisplay blue image data, one for a 3 m depth plane and the other for a 1m depth plane, and two eyepiece waveguides 1104 designed to displaygreen image data, one for a 3 m depth plane and the other for a 1 mdepth plane. Each of these six eyepiece waveguides 1104 is illustratedas being 0.325 mm thick, though other thicknesses are also possible.

A world-side cover window 1102 and an eye-side cover window 1106 arealso shown in FIG. 11. These cover windows can be, for example, 0.330 mmthick. When accounting for the thickness of the six eyepiece waveguides1104, the seven air gaps, the two cover windows 1102, 1106, and the edgeseal 1108, the total thickness of the illustrated eyepiece waveguidestack 1100 is 2.8 mm.

K-Space Representations of AR Eyepiece Waveguides

FIGS. 12A and 12B illustrate top views of an eyepiece waveguide 1200 inoperation as it projects an image toward a user's eye 210. The image canfirst be projected from an image plane 1207 toward an entrance pupil1208 of the eyepiece waveguide 1200 using a projection lens 1210 or someother projector device. Each image point (e.g., an image pixel or partof an image pixel) has a corresponding input beam of light (e.g., 1202a, 1204 a, 1206 a) which propagates in a particular direction at theentrance pupil 1208 (e.g., at a particular angle with respect to theoptical axis of the projector lens 1210). Although illustrated as rays,the input beams of light 1202 a, 1204 a, 1206 a may be, for example,collimated beams with diameters of a few millimeters or less when theyenter the eyepiece waveguide 1200.

In FIGS. 12A and 12B, a middle image point corresponds to input beam1204 a, which is illustrated with a solid line. A right-hand image pointcorresponds to input beam 1202 a, which is illustrated with a dashedline. And a left-hand image point corresponds to input beam 1206 a,which is illustrated with a dash-dot line. For clarity of illustration,only three input beams 1202 a, 1204 a, 1206 a are shown at the entrancepupil 1208, though a typical input image will include many input beamspropagating at a range of angles, both in the x-direction and they-direction, which correspond to different image points in atwo-dimensional image plane.

There is a unique correspondence between the various propagation anglesof the input beams (e.g., 1202 a, 1204 a, 1206 a) at the entrance pupil1208 and the respective image points at the image plane 1207. Theeyepiece waveguide 1200 can be designed to in-couple the input beams(e.g., 1202 a, 1204 a, 1206 a), replicate them in a distributed mannerthrough space, and guide them to form an exit pupil 1210, which islarger than the entrance pupil 1208 and is made up of the replicatedbeams, all while substantially maintaining the correspondence betweenimage points and beam angles. The eyepiece waveguide 1200 can convert agiven input beam of light (e.g., 1202 a), which propagates at aparticular angle, into many replicated beams (e.g., 1202 b) which areoutput across the exit pupil 1210 at an angle that is substantiallyuniquely correlated with that particular input beam and itscorresponding image point. For example, the replicated output beamscorresponding to each input beam can exit the eyepiece waveguide 1200 atsubstantially the same angle as their corresponding input beam.

As shown in FIGS. 12A and 12B, the input beam of light 1204 acorresponding to the middle image point at the image plane 1207 isconverted into a set of replicated output beams 1204 b, shown with solidlines, which are aligned with an optical axis perpendicular to the exitpupil 1210 of the eyepiece waveguide 1200. The input beam of light 1202a corresponding to the right-hand image point at the image plane 1207 isconverted into a set of replicated output beams 1202 b, shown withdashed lines, which exit the eyepiece waveguide 1200 at a propagationangle such that they appear to have originated from a location in theright-hand portion of the user's field of view. Similarly, the inputbeam of light 1206 a corresponding to the left-hand image point at theimage plane 1207 is converted into a set of replicated output beams 1206b, shown with dash-dot lines, which exit the eyepiece waveguide 1200 ata propagation angle such that they appear to have originated from alocation in the left-hand portion of the user's field of view. Thegreater the range of input beam angles and/or output beam angles, thegreater the field of view (FOV) of the eyepiece waveguide 1200.

For each image, there are sets of replicated output beams (e.g., 1202 b,1204 b, 1206 b)—one set of replicated beams per image point—which areoutput across the exit pupil 1210 at different angles. The individualoutput beams (e.g., 1202 b, 1204 b, 1206 b) can each be collimated. Theset of output beams corresponding to a given image point may consist ofbeams which propagate along parallel paths (as shown in FIG. 12A) ordiverging paths (as shown in FIG. 12B). In either case, the specificpropagation angle of the set of replicated output beams depends on thelocation of the corresponding image point at the image plane 1207. FIG.12A illustrates the case where each set of output beams (e.g., 1202 b,1204 b, 1206 b) consists of beams which propagate along parallel paths.This results in the image being projected so as to appear to haveoriginated from optical infinity. This is represented in FIG. 12A by thefaint lines extending from the peripheral output beams 1202 b, 1204 b,1206 b toward optical infinity on the world-side of the eyepiecewaveguide 1200 (opposite the side where the user's eye 210 is located).FIG. 12B illustrates the case where each set of output beams (e.g., 1202b, 1204 b, 1206 b) consists of beams which propagate along divergingpaths. This results in the image being projected so as to appear to haveoriginated from a virtual depth plane having a distance closer thanoptical infinity. This is represented in FIG. 12B by the faint linesextending from the peripheral output beams 1202 b, 1204 b, 1206 b towardpoints on the world-side of the eyepiece waveguide 1200.

Again, each set of replicated output beams (e.g., 1202 b, 1204 b, 1206b) has a propagation angle that corresponds to a particular image pointat the image plane 1207. In the case of a set of replicated output beamswhich propagate along parallel paths (see FIG. 12A), the propagationangles of all the beams are the same. In the case of a set of replicatedoutput beams which propagate along diverging paths, however, theindividual output beams can propagate at different angles, but thoseangles are related to one another in that they create an aggregatediverging wavefront and appear to have originated from a common pointalong the axis of the set of beams (See FIG. 12B). It is this axis whichdefines the angle of propagation for the set of diverging output beamsand which corresponds to a particular image point at the image plane1207.

The various beams of light entering the eyepiece waveguide 1200,propagating within the eyepiece waveguide, and exiting the eyepiecewaveguide can all be described using one or more wave vectors, ork-vectors, which describe a beam's direction(s) of propagation. K-spaceis an analytical framework which relates k-vectors to geometricalpoints. In k-space, each point in space corresponds to a uniquek-vector, which in turn can represent a beam or ray of light with aparticular propagation direction. This allows the input and outputbeams, with their corresponding propagation angles, to be understood asa set of points (e.g., a rectangle) in k-space. The diffractive featureswhich change the propagation directions of the light beams whiletraveling through the eyepiece can be understood in k-space as simplytranslating the location of the set of k-space points which make up theimage. This new translated k-space location corresponds to a new set ofk-vectors, which in turn represent the new propagation angles of thebeams or rays of light after interacting with the diffractive features.

The operation of an eyepiece waveguide can be understood by the mannerin which it causes a set of points, such as the points inside a k-spacerectangle which correspond to a projected image, to move in k-space.This is in contrast to more complicated ray tracing diagrams which mightotherwise be used to illustrate the beams and their propagation angles.K-space is therefore an effective tool for describing the design andoperation of eyepiece waveguides. The following discussion describes thek-space representation of features and functions of various AR eyepiecewaveguides.

FIG. 13A illustrates a k-vector 1302 which can be used to represent thepropagation direction of a light ray or a light beam. The particularillustrated k-vector 1302 is representative of a plane wave with planarwavefronts 1304. The k-vector 1302 points in the propagation directionof the light ray or beam which it represents. The magnitude, or length,of the k-vector 1302 is defined by a wavenumber, k. The dispersionequation, ω=ck, relates the angular frequency, ω, of the light, thespeed of the light, c, and the wavenumber, k. (In a vacuum, the speed ofthe light is equal to the speed of light constant, c. In a medium,however, the speed of the light is inversely proportional to therefractive index of the medium. Thus, in a medium the equation becomesk=nω/c.) Note that by definition, k=2π/λ and ω=2πf, where f is thefrequency of light (e.g. in units of Hertz). As is evident from thisequation, light beams with higher angular frequencies, w, have largerwavenumbers, and thus larger-magnitude k-vectors (assuming the samepropagation medium). For instance, assuming the same propagation medium,blue light beams have larger-magnitude k-vectors than red light beams.

FIG. 13B illustrates a light ray 1301 corresponding to the k-vector 1302within a planar waveguide 1300. The waveguide 1300 can be representativeof any of the waveguides described herein and may be part of an eyepiecefor an AR display system. The waveguide 1300 can guide light rays havingcertain k-vectors via total internal reflection (TIR). For example, asshown in FIG. 13B, the light ray 1301 illustrated by k-vector 1302 isdirected toward the upper surface of the waveguide 1300 at an angle. Ifthe angle is not too steep, as governed by Snell's law, then the lightray 1301 will reflect at the upper surface of the waveguide 1300, at anangle equal to the angle of incidence, and then propagate down towardthe lower surface of the waveguide 1300 where it will reflect again backtowards the upper surface. The light ray 1301 will continue propagatingin a guided fashion within the waveguide 1300, reflecting back and forthbetween its upper and lower surfaces.

FIG. 13C illustrates the permissible k-vectors for light of a givenangular frequency, ω, propagating in an unbounded homogenous medium withrefractive index, n. The length, or magnitude, k, of the illustratedk-vector 1302 is equal to the refractive index, n, of the medium timesthe angular frequency, ω, of the light divided by the speed of lightconstant, c. For light rays or beams with a given angular frequency, ω,propagating in a homogeneous medium with refractive index, n, themagnitudes of all permissible k-vectors are the same. And for unguidedpropagation, all propagation directions are permitted. Therefore, themanifold in k-space which defines all permissible k-vectors is a hollowsphere 1306, where the size of the sphere is dependent upon the angularfrequency of the light and the refractive index of the medium.

FIG. 13D illustrates the permissible k-vectors for light of a givenangular frequency, ω, propagating in a homogenous planar waveguidemedium with refractive index, n. Whereas in an unbound medium, allpermissible k-vectors lie on the hollow sphere 1306, to determine thepermissible k-vectors in a planar waveguide, we can project the sphere1306 of permissible k-vectors onto a plane (e.g., the x-y plane). Thisresults in a solid disk 1308 in projected k-space, which represents thek-vectors which can propagate within a planar waveguide. As shown inFIG. 13D, the k-vectors which can propagate within a planar waveguide inthe x-y plane (e.g., waveguide 1300) are all those for which thecomponent of the k-vector in the x-y plane is less than or equal to therefractive index, n, of the medium times the angular frequency, ω, ofthe light divided by the speed of light constant, c.

Every point within the solid disk 1308 corresponds to the k-vector of awave which can propagate in the waveguide (though not all of thesek-vectors result in guided propagation within the waveguide, asdiscussed below with respect to FIG. 13E). At each point within thesolid disk 1308, there are two permitted waves: one with a z-componentof propagation into the page, and another with a z-component ofpropagation out of the page. Therefore the out-of-plane component of thek-vector, k_(z), may be recovered using the equation k_(z)=±√{squareroot over (|k|²−k_(x) ²−k_(y) ²)}, where the sign chosen determineswhether the wave is propagating into or out of the page. Since all lightwaves of a given angular frequency, ω, propagating in a homogeneousmedium with refractive index, n, have the same magnitude k-vector, lightwaves with k-vectors whose x-y components are closer in size to theradius of the solid disk 1308 have smaller z-components of propagation(resulting in the less steep propagation angles necessary for TIR, asdiscussed with respect to FIG. 13B), while light waves with k-vectorswhose x-y components are located closer to the center of the solid disk1308 have larger z-components of propagation (resulting in steeperpropagation angles which may not TIR). Henceforth, all mentions ofk-space refer to the projected k-space (unless otherwise evident fromcontext), in which the 2-dimensional k-plane corresponds to the plane ofthe waveguide; unless the propagation direction between surfaces of thewaveguide is explicitly mentioned, the discussion and drawings generallyonly consider the directions parallel to the surfaces of the waveguide.Furthermore, when plotting k-space, it is typically most convenient tonormalize the free-space disk radius to unity, so that plots areeffectively normalized to co/c.

FIG. 13E illustrates an annulus 1310 in k-space which corresponds tok-vectors of light waves which can be guided within a waveguide having arefractive index, n₂ (e.g., n₂=1.5). The waveguide is physicallysurrounded by a medium (e.g., air) having a lesser refractive index, n₁(e.g., n₁≈1). As just discussed with respect to FIG. 13D, the k-vectorscorresponding to permitted waves within a planar waveguide medium in thex-y plane are all those k-vectors whose respective x-y components lie ina solid disk 1308 in k-space. The radius of the solid disk 1308 isproportional to the refractive index of the waveguide medium. Thus, withreference back to FIG. 13E, the k-vectors which correspond to lightwaves which can propagate in a planar waveguide medium having refractiveindex n₂=1.5 are those whose respective x-y components lie within thelarger disk 1308 a. Meanwhile, the k-vectors which correspond to lightwaves which can propagate in the surrounding medium having refractiveindex n₁=1 are those whose respective x-y components lie within thesmaller disk 1308 b. All k-vectors whose respective x-y components lieinside the annulus 1310 correspond to those light waves which canpropagate in the waveguide medium but not in the surrounding medium(e.g., air). These are the light waves which are guided in the waveguidemedium via total internal reflection, as described with respect to FIG.13B. Thus, light rays or beams can only undergo guided propagationwithin a waveguide of an AR eyepiece if they have k-vectors which lie inthe k-space annulus 1310. Note that propagating light waves havingk-vectors outside of the larger disk 1308 a are forbidden; there are nopropagating waves whose k-vectors lie in that region (waves in thatregion have evanescently decaying, rather than constant, amplitude alongtheir propagation direction).

The various AR eyepiece waveguides described herein can in-couple lightby using diffractive features, such as diffractive structures, to directthe k-vectors of light beams propagating in free space (n₁≈1) (e.g.,from a projector) into the k-space annulus 1310 of an eyepiecewaveguide. Any light wave whose k-vector lies in the annulus 1310 canpropagate in guided fashion within the eyepiece waveguide. The width ofthe annulus 1310 determines the range of k-vectors—and, hence, the rangeof propagation angles—which can be guided within the eyepiece waveguide.Thus, the width of the k-space annulus 1310 has typically been thoughtto determine the maximum field of view (FOV) which can be projected bythe eyepiece waveguide. Since the width of the annulus 1310 depends onthe radius of the larger disk 1308 a, which is itself partiallydependent upon the refractive index, n₂, of the eyepiece waveguidemedium, one technique for increasing eyepiece FOV is to use an eyepiecewaveguide medium with a larger refractive index (in comparison to therefractive index of the medium surrounding the eyepiece waveguide).There are, however, practical limitations on the refractive indexes ofwaveguide media which can be used in AR eyepieces, such as materialcost. This in turn has been thought to place practical limitations onthe FOV of AR eyepieces. But, as explained herein, there are techniqueswhich can be used to overcome these limitations so as to allow forlarger FOVs.

Although the radius of the larger disk 1308 a in FIG. 13E is alsodependent on the angular frequency, ω, of the light, and the width ofthe annulus 1310 therefore depends on the color of the light, this doesnot imply that the FOV supported by the eyepiece waveguide is larger forlight with higher angular frequencies, since any given angular extentcorresponding to the FOV scales in direct proportion to the angularfrequency as well.

FIG. 13F shows a k-space diagram similar to that depicted in FIG. 13E.The k-space diagram shows a smaller disk 1308 b corresponding topermissible k-vectors in a first medium of refractive index n₁, a largerdisk 1308 a corresponding to permissible k-vectors in a second medium ofrefractive index n₂ (n₂>n₁), and an annulus 1310 between the outerboundaries of smaller disk 1308 a and larger disk 1308 b. Although allk-vectors in the width 1342 of the annulus 1310 correspond to guidedpropagation angles, it is possible that fewer than all of the k-vectorsthat lie within the width 1342 of the annulus 1310 may be satisfactoryfor use in displaying an image.

FIG. 13F also shows a waveguide 1350 with two guided beams shown incomparison to one another. The first light beam has a first k-vector1344 a near the outer edge of the annulus 1310. The first k-vector 1344a corresponds to a first TIR propagation path 1344 b shown in across-sectional view of the waveguide 1350 having refractive index n₂surrounded by air of refractive index n₁. A second light beam is alsoshown that has a second k-vector 1346 a closer to the center of thek-space annulus 1310. The second k-vector 1346 a corresponds to a secondTIR propagation path 1346 b in the waveguide 1350. The waveguide 1350may include a diffraction grating 1352 on or within the waveguide 1350.When a light beam encounters the surface of the waveguide 1350 with thediffraction grating 1352, an interaction occurs which may send a sampleof the light beam energy out of the waveguide while the beam continuesto TIR in the waveguide. The angle at which a light beam propagates inTIR through the waveguide determines the density of reflection events,or the number of bounces per unit length against the surface of thewaveguide 1350 with the diffraction grating 1352. Returning to theexample of the light beam comparison, the first light beam in the firstTIR propagation path 1344 b reflects from the waveguide surface with thediffraction grating 1352 four times to produce four exit pupils 1354(illustrated with solid lines) over the length of the diffractiongrating 1352, while the second light beam in the second TIR propagationpath 1346 b reflects from the waveguide surface with diffraction grating1352 ten times, over the same or similar distance, to produce ten exitpupils 1356 (illustrated with dashed lines) across the length of thediffraction grating 1352.

In practice, it may be desirable to constrain the output beam, or exitpupil spacing, to be equal to, or within, a pre-selected range to ensurethat a user will see the projected content from any position within thepre-defined eye box. With this information, it is possible to limit thewidth 1342 of the annulus 1310 to a subset 1344 of k-vectors for whichthis constraint holds, and to disqualify angles that are too grazingfrom being included in the design calculations. More or fewer anglesthan the subset 1344 may be acceptable depending on desired performance,diffraction grating design, and other optimization factors. Similarly,in some embodiments, k-vectors corresponding to propagation angles thatare too steep with respect to the surface of the waveguide and providetoo many interactions with the diffraction grating 1352 may also bedisqualified from use. In such embodiments, the width 1342 of theannulus 1310 can be decreased by effectively moving the boundary ofusable angles radially outward from the boundary between the larger disk1308 a and the smaller disk 1308 b. The designs of any of the eyepiecewaveguides disclosed herein can be adjusted by constraining the width ofthe k-space annulus 1310 in this way.

As described above, k-vectors, within the annulus 1310, corresponding tosuboptimal TIR propagation pathways may be omitted from use in eyepiecedesign calculations. Alternatively, k-vectors corresponding to TIRpropagation pathways with too grazing of an angle, and thus too low of adensity of reflection events on the surface of the waveguide with adiffraction grating, may be compensated for using various techniquesdescribed herein. One technique is to use an in-coupling grating todirect portions of the field of view (FOV) of the incoming image to twodifferent areas of the k-space annulus 1310. In particular, it may beadvantageous to direct the incoming image to a first side of the k-spaceannulus 1310, represented by a first group of k-vectors, and to a secondside of the k-space annulus 1310, represented by a second group ofk-vectors, where the first and second sides of the k-space annulus 1310are substantially opposed from one another. For example, the first groupof k vectors may correspond to an FOV rectangle of k-vectors on the leftside of the annulus 1310 and the second group of k-vectors maycorrespond to an FOV rectangle of k-vectors on the right side of theannulus 1310. The left FOV rectangle has its left edge near the outeredge of larger disk 1308 a, corresponding to near-grazing k-vectorangles. Light at this edge would produce sparse exit pupils. However,the same left edge of the right FOV rectangle, located on the right sideof the annulus 1310, would be nearer to the center of the larger disk1308 a. Light at the same left edge of the right FOV rectangle wouldhave a high density of exit pupils. Thus, when the left and right FOVrectangles are rejoined exiting the waveguide toward the user's eye toproduce an image, a sufficient number of exit pupils are produced at allareas of the field of view.

Diffractive features, such as diffraction gratings, can be used tocouple light into an eyepiece waveguide, out of an eyepiece waveguide,and/or to change the propagation direction of light within the eyepiecewaveguide. In k-space, the effect of a diffraction grating on a ray orbeam of light represented by a particular k-vector is determined byvector addition of the k-vector component in the plane of thediffraction grating with a grating vector. The magnitude and directionof the grating vector depend on the specific properties of thediffraction grating. FIGS. 13G, 13H, and 13I illustrate the operation ofdiffraction gratings on k-vectors in k-space.

FIG. 13G illustrates a top view of a diffraction grating 1320 and someof its associated k-space diffraction grating vectors (G⁻², G⁻¹, G₁,G₂). The diffraction grating 1320 is oriented in the x-y plane and FIG.13G shows the view of the grating from the perspective of a light ray orbeam which is incident upon it from the z-direction. The diffractiongrating 1320 has an associated set of k-space diffraction gratingvectors (e.g., G⁻², G⁻¹, G₁, G₂) which are oriented in the same plane asthe diffraction grating. The G₁ and G⁻¹ grating vectors correspond tothe ±1 diffractive orders, respectively, while the G₂ and G⁻² gratingvectors correspond to the ±2 diffractive orders, respectively. Thegrating vectors for the ±1 diffractive orders point in oppositedirections (along the axis of periodicity of the grating) and have equalmagnitudes which are inversely proportional to the period, Λ, of thediffraction grating 1320. Thus, a diffraction grating with a finer pitchhas larger grating vectors. The grating vectors for the ±2 diffractiveorders also point in opposite directions and have equal magnitudes whichare twice that of the grating vectors for the ±1 diffractive orders.There can also be grating vectors for additional higher diffractiveorders, though they are not illustrated. For example, the magnitudes ofthe grating vectors for the ±3 diffractive orders are three times thatof the grating vectors for the ±1 diffractive orders, and so on. Notethat the fundamental grating vector G₁ is determined solely by theperiodicity of the grating (direction and pitch), while the compositionof the grating (e.g., surface profile, materials, layer structure) mayaffect other characteristics of the grating, such as diffractionefficiency and diffracted phase. Since all the harmonics of thefundamental grating vector (e.g., G⁻¹, G₂, G⁻², etc.) are simply integermultiples of the fundamental G₁, then all diffraction directions of thegrating are solely determined by the periodicity of the grating. Theaction of the diffraction grating 1320 is to add the grating vectors tothe in-plane component of the k-vector corresponding to the incidentlight ray or beam. This is shown in FIG. 13H.

FIG. 13H illustrates a transverse view of the diffraction grating 1320and its effect, in k-space, on a k-vector 1302 corresponding to anormally-incident ray or beam of light. The diffraction grating 1320diffracts the incident ray or beam of light into one or more diffractiveorders. The new ray or beam of light in each of these diffractive ordersis represented by a new k-vector (e.g., 1302 a-e). These new k-vectors(e.g., 1302 a-e) are determined by vector addition of the in-planecomponent of the k-vector 1302 with each of the grating vectors (e.g.,G⁻², G⁻¹, G₁, G₂). In the illustrated case of a normally-incident ray orbeam of light, the k-vector 1302 has no component in the x-y plane ofthe diffraction grating. As such, the effect of the diffraction grating1320 is to create one or more new diffracted rays or beams of lightwhose k-vectors (e.g., 1302 a-e) have x-y components equal to thecorresponding grating vector. For example, the x-y components of the ±1diffractive orders of the incident ray or beam of light become G₁ andG⁻¹, respectively. Meanwhile, the magnitudes of the new k-vectors areconstrained to be 2π/ω, so the new k-vectors (e.g., 1302 a-e) all lie ona semi-circle, as shown in FIG. 13H. Since the in-plane component of theincoming k-vector 1302 is being added to grating vectors whose lengthsare equal to a fundamental increment, or 2× the fundamental increment,etc., whereas the magnitude of each resulting k-vector is constrained,the angles between the k-vectors (e.g., 1302 a-e) for the variousdiffractive orders are not equal; rather the k-vectors (e.g., 1302 a-e)become more angularly sparse with increasing diffractive order.

In the case of diffraction gratings formed on or in a planar eyepiecewaveguide, the in-plane components of the new k-vectors (e.g., 1302 a-e)may be of most interest because if they lie in the k-space annulus 1310of the eyepiece waveguide, then the diffracted rays or beams of lightwill undergo guided propagation through the eyepiece waveguide. But ifthe in-plane components of the new k-vectors (e.g., 1302 a-e) lie in thecentral disk 1308 b, then the diffracted rays or beams of light willexit the eyepiece waveguide.

FIG. 13I illustrates a transverse view of the diffraction grating 1320and its effect, in k-space, on a k-vector 1302 corresponding to anobliquely-incident ray or beam of light. The effect is similar to thatdescribed with respect to FIG. 13H. Specifically, the k-vectors of thediffracted rays or beams of light are determined by vector addition ofthe in-plane component of the incident k-vector with the grating vectors(G⁻², G⁻¹, G₁, G₂). For an obliquely-incident k-vector 1302, thecomponent of the k-vector in the x-y plane of the diffraction grating1320 is non-zero. This component is added to the grating vectors todetermine the in-plane components of the new k-vectors for thediffracted rays or beams of light. The magnitudes of the new k-vectorsare constrained to be 2π/ω. And, once again, if the in-plane componentsof the k-vectors of the diffracted rays or beams of light lie in thek-space annulus 1310 of the eyepiece waveguide, then the diffracted raysor beams of light will undergo guided propagation through the eyepiecewaveguide.

FIG. 13J is a k-space diagram which illustrates the field of view (FOV)of an image that is projected into an AR eyepiece waveguide (e.g., 1200,1300). The k-space diagram includes a larger disk 1308 a, which definesthe k-vectors of light beams or rays that can propagate within theeyepiece waveguide. The k-space diagram also includes a smaller disk1308 b, which defines the k-vectors of light beams or rays which canpropagate within a medium, such as air, that surrounds the eyepiecewaveguide. And, as already discussed, the k-space annulus 1310 definesthe k-vectors of light beams or rays that can undergo guided propagationwithin the eyepiece waveguide.

The input beams (e.g., 1202 a, 1204 a, 1206 a) which are projected intothe entrance pupil of the eyepiece waveguide are shown in FIGS. 12A and12B. Each input beam has a propagation angle which is uniquely definedby the spatial location of a corresponding image point in the imageplane. The set of input beams have a certain angular spread in both thex-direction and the y-direction. The angular spread in the x-directioncan define a horizontal field of view, while the angular spread in they-direction can define a vertical field of view. In addition, theangular spread of the input beams along, for example, the diagonalbetween the x-direction and the y-direction can define a diagonal fieldof view.

In k-space, the field of view of the input image can be approximated byan FOV rectangle 1330. The FOV rectangle 1330 encloses a set ofk-vectors which corresponds to the set of input light beams. The FOVrectangle 1330 has a dimension along the k_(x)-axis which corresponds tothe angular spread of the input beams in the x-direction. Specifically,the horizontal width of the FOV rectangle 1330 is 2n·sin

$\left( \frac{\theta_{x}}{2} \right),$

where θ_(x) is the total horizontal FOV and n is the refractive index ofthe incident medium. The FOV rectangle 1330 also has a dimension alongthe k_(y)-axis which defines the angular spread of the input beams inthe y-direction. Similarly, the vertical height of the FOV rectangle1330 is 2n·sin

$\left( \frac{\theta_{y}}{2} \right),$

where θ_(y) is the total vertical FOV. Although a rectangle is shown asrepresenting the set of input beams, in some embodiments the set ofinput beams could be such that it would correspond to a different shapein k-space. But the k-space analyses herein which are generally shownusing FOV rectangles or FOV squares can equally apply to other shapes ink-space as well.

As shown in FIG. 13J, the FOV rectangle 1330 is centered on, and locatedcompletely within, the smaller disk 1308 b. This position of the FOVrectangle 1330 corresponds to the k-vectors of a set of input beams(e.g., in a configuration with on-axis, or telecentric, projection fromthe image source) or a set of output beams propagating generally in the±z-direction (although the set of beams is centered on the z-axis, allof the beams—except those normal to the entrance pupil or exitpupil—have some amount of angular deviation relative to the±z-direction). In other words, when the FOV rectangle 1330 is within thesmaller disk 1308 b in a k-space diagram, it can represent the inputbeams as they propagate from an image source, through free space, to theeyepiece waveguide. It can also represent the output beams as theypropagate from the eyepiece waveguide to the user's eye. Each k-spacepoint within the FOV rectangle 1330 corresponds to a k-vector whichrepresents one of the input beam directions or one of the output beamdirections. In order for the input beams represented by the FOVrectangle 1330 to undergo guided propagation within the eyepiecewaveguide, the FOV rectangle 1330 must be translated to the k-spaceannulus 1310. Conversely, in order for the output beams represented bythe FOV rectangle 1330 to exit the eyepiece waveguide, the FOV rectangle1330 must be translated from the k-space annulus 1310 back to thesmaller disk 1308 b. In order to not introduce geometric and chromaticdispersion from propagation through the waveguide, the FOV rectangle1330 of the input beams may coincide with the FOV rectangle of theoutput beams; in this configuration the eyepiece waveguide preservesbeam angles from input to output.

The following equations describe the FOV which may be achieved in someeyepiece waveguides:

$\theta_{x} = {{arc}\; {\sin \left( \frac{k_{x}}{k} \right)}}$FOV_(x) = max (θ_(x, air)) − min (θ_(x, air))${FOV}_{x} = {{{arc}\; {\sin \left( \frac{\max \left( {k_{x,{air}}} \right)}{k_{air}} \right)}} - {\arcsin \left( \frac{\min \left( {k_{x,{air}}} \right)}{k_{air}} \right)}}$

If the FOV is horizontally centered at θ_(x)=0, then a conventionaleyepiece waveguide may have the following limit:

${\max \left( {FOV}_{x} \right)} = {2 \times {arc}\; {\sin \left( \frac{\max \left( {k_{x,{air}}} \right)}{k_{air}} \right)}}$${\max \left( {FOV}_{x} \right)} = {2 \times {arc}\; {\sin \left( \frac{\frac{1}{2} \times \frac{w}{c}\left( {n_{2} - n_{air}} \right)}{\frac{w}{c}n_{air}} \right)}}$${\max \left( {FOV}_{x} \right)} = {2 \times {arc}\; {\sin \left( {\frac{1}{2}\left( {n_{2} - 1} \right)} \right)}}$

The only dependence of max(FOV_(x)) on angular frequency is from thewaveguide refractive index's dependence on angular frequency, which maybe an important detail in some applications but often has a relativelysmall effect.

FIG. 13K is a k-space diagram which shows the translational shift, ink-space, of the FOV rectangle 1330 which is caused by an input couplinggrating (ICG) located at the entrance pupil of the eyepiece waveguide.The ICG has associated diffraction grating vectors (G⁻¹, G₁), as justdiscussed with respect to FIGS. 13G-13I. The ICG diffracts each of theinput beams represented by the FOV rectangle 1330 into a +1 diffractiveorder and a −1 diffractive order. In k-space, the diffraction of theinput beams into the +1 diffractive order is represented by the FOVrectangle 1330 being displaced in the k_(x)-direction by the G₁ gratingvector. Similarly, in k-space, the diffraction of the input beams intothe −1 diffractive order is represented by the FOV rectangle 1330 beingdisplaced in the −k_(x)-direction by the G⁻¹ grating vector.

For the particular example shown in FIG. 13K, the translated FOVrectangles are too large to fit entirely within the k-space annulus1310. This means that the eyepiece waveguide cannot support all of theinput beams in the FOV in guided propagation modes, whether in thepositive or negative diffractive order, because the angular spreadbetween them is too large. The k-vectors corresponding to points in thetranslated FOV rectangles which lie outside the larger disk 1308 a wouldnot be diffracted at all by the ICG because those k-vectors are notpermitted. (This would also prevent diffraction into the ±2 and higherdiffractive orders in this case because the grating vectors associatedwith those orders are even longer and would therefore translate thek-vectors even further outside the larger disk 1308 a.) Meanwhile, ifany part of the translated FOV rectangles were to still lie inside thesmaller disk 1308 b after translation by the ICG, then the light beamscorresponding to those particular k-vectors would exit the eyepiecewaveguide by transmitting through its planar face for failure to TIR andwould not undergo guided propagation through the waveguide.

One possible modification which could be made in order to support moreof the input beams of light represented by the translated FOV rectangles1330 in guided modes may be to increase the difference between therefractive index of the eyepiece waveguide and that of the surroundingmedium. This would increase the size of the larger disk 1308 a and/ordecrease the size of the smaller disk 1308 b (a decrease in the size ofthe smaller disk 1308 b is possible if the waveguide is not surroundedby air), thereby increasing the size of the k-space annulus 1310.

Example AR Eyepiece Waveguides with Orthogonal Pupil Expanders

FIG. 14A illustrates an example eyepiece waveguide 1400 with an ICGregion 1440, an orthogonal pupil expander (OPE) region 1450, and an exitpupil expander (EPE) region 1460. FIG. 14B includes k-space diagramswhich illustrate the effect of each of these components of the eyepiecewaveguide 1400 in k-space. The ICG region 1440, OPE region 1450, and EPEregion 1460 of the eyepiece waveguide 1400 include various diffractivefeatures which couple input beams into the eyepiece waveguide topropagate via guided modes, replicate the beams at multiple distributedlocations in space, and cause the replicated beams to exit the eyepiecewaveguide and be projected toward the user's eye.

Input beams corresponding to an input image can be projected into theeyepiece waveguide 1400 from one or more input devices. The input beamscan be incident on the ICG region 1440, which can coincide with theentrance pupil of the eyepiece waveguide 1400. The input device used toproject the input beams can include, for example, a spatial lightmodulator projector (located in front of, or behind, the eyepiecewaveguide 1400 with respect to the user's face). In some embodiments,the input device may use liquid crystal display (LCD), liquid crystal onsilicon (LCoS), fiber scanned display (FSD) technology, or scannedmicroelectromechanical systems (MEMS) mirror displays, though others canalso be used. Input beams from the input device are projected into theeyepiece waveguide 1400, generally in the illustrated −z-direction, atvarious propagation angles and are incident on the ICG region 1440 fromoutside the substrate of the eyepiece waveguide.

The ICG region 1440 includes diffractive features which redirect theinput beams such that they propagate inside the eyepiece waveguide 1400via total internal reflection. In some embodiments, the diffractivefeatures of the ICG region 1440 may form a one-dimensionally periodic(1D) diffraction grating made up of many lines which extend verticallyin the illustrated y-direction and periodically repeat horizontally inthe illustrated x-direction. In some embodiments, the lines may beetched into the front or back surface of the eyepiece waveguide 1400and/or they may be formed of material deposited onto the front or backsurface. The period, duty cycle, depth, profile, blaze angle, etc. ofthe lines can be selected based on the angular frequency, ω, of lightfor which the eyepiece waveguide 1400 is designed, the desireddiffractive efficiency of the grating, and other factors. In someembodiments, the ICG region 1440 is designed to primarily couple inputlight into the +1 and −1 diffractive orders. (The diffraction gratingcan be designed so as to reduce or eliminate the 0^(th) diffractiveorder and higher diffractive orders beyond the first diffractive orders.This can be accomplished by appropriately shaping the profile of eachline. In many practical ICGs in AR displays, however, all higherdiffractive orders correspond to k-vectors which lie beyond the k-spaceannulus. Thus, those higher diffractive orders would be forbiddenregardless of non-k-space attributes like grating duty cycle, depth, andprofile.) The diffracted beams in one of the ±1 diffractive orders fromthe ICG region 1440 then propagate generally in the −x-direction towardthe OPE region 1450, while the diffracted beams in the other of the ±1diffractive orders then propagate generally in the +x-direction and exitthe eyepiece waveguide 1400.

The OPE region 1450 includes diffractive features which can perform atleast two functions: first, they can perform pupil expansion byspatially replicating each input beam of light at many new locationsgenerally in the −x-direction; second, they can guide each replicatedbeam of light on a path generally toward the EPE region 1460. In someembodiments, these diffractive features are lines formed on or in thesubstrate of the eyepiece waveguide 1400. The period, duty cycle, depth,profile, blaze angle, etc. of the lines can be selected based on theangular frequency, ω, of light for which the eyepiece waveguide 1400 isdesigned, the desired diffractive efficiency of the grating, and otherfactors. The specific shape of the OPE region 1450 can vary, but ingeneral it may be determined based on the fan out of the beams of lightfrom the ICG region 1440 and on the size and location of the EPE region1460. This is discussed further with respect to FIG. 14D.

The diffraction grating of the OPE region 1450 can be designed withrelatively low and/or variable diffractive efficiency. These propertiescan allow the OPE region 1450 to replicate each beam of light thatarrives from the ICG region 1440 and/or to more evenly distribute thelight energy in at least one dimension. Because of the relatively lowdiffractive efficiency, each interaction of a beam of light with thegrating diffracts only a portion of the power in the light beam whilethe remaining portion continues to propagate in the same direction.(Some parameters that can be used to influence the diffractiveefficiency of the grating are the height and width of the line features,or magnitude of refractive index difference between the line featuresand the background medium.) That is, when a beam interacts with thediffraction grating in the OPE region 1450, a portion of its power willbe diffracted toward the EPE region 1460 while the remaining portionwill continue to transmit within the OPE region to encounter the gratingagain at a different spatial location, where another portion of thebeam's power may be diffracted toward the EPE region 1460, and so on.Since some portions of the power of each light beam travel furtherthrough the OPE region 1450 than others before being diffracted towardthe EPE region 1460, there are numerous copies of the incoming beamtraveling towards the EPE region from different locations in the−x-direction. The spatial extent of the replicated beams, in thedirection of propagation of the original incoming beam through the OPEregion 1450, therefore effectively increases, while the intensity of theincoming beam correspondingly decreases because the light which made upthe input beam is now divided amongst many replicated beams.

The diffraction grating in the OPE region 1450 is obliquely orientedwith respect to the beams arriving from the ICG region 1440 so as todiffract the beams generally toward the EPE region 1460. The specificangle of the slant of the diffraction grating in the OPE region 1450 maydepend upon the layout of the various regions of the eyepiece waveguide1400 and can perhaps be seen more clearly in the k-space diagrams foundand discussed later in FIG. 14B. In the eyepiece waveguide 1400, the ICGregion 1440 is located to the right of the OPE region 1450, while theEPE region 1460 is located below the OPE region. Therefore, in order tore-direct light from the ICG region 1440 toward the EPE region 1460, thediffraction grating of the OPE region 1450 may be oriented at about 45°with respect to the illustrated x-axis.

FIG. 14C is a three-dimensional illustration of the optical operation ofthe OPE region 1450 shown in FIGS. 14A and 14B. FIG. 14C shows the ICGregion 1440 and the OPE region 1450, both on the side of the waveguidethat is closer to the viewer. The grating lines cannot be seen becausethey are microscopic. In this case, a single input beam 1401 isillustrated, but an image will be made up of many such input beamspropagating through the eyepiece waveguide 1400 in slightly differentdirections. The input beam 1401 enters the OPE region 1450 from the ICGregion 1440. The input beam 1401 then continues to propagate through theeyepiece waveguide 1400 via total internal reflection, repeatedlyreflecting back and forth between its surfaces. This is represented inFIG. 14C by the zig-zagging in the illustrated propagation of each beam.

When the input beam 1401 interacts with the diffraction grating formedin the OPE region 1450, a portion of its power is diffracted toward theEPE region, while another portion of its power continues along the samepath through the OPE region 1450. As already mentioned, this is due inpart to the relatively low diffractive efficiency of the grating.Further, beams diffracted toward the EPE region may re-encounter thegrating of the OPE region 1450 and diffract back into the originaldirection of propagation of the input beam 1401. The paths of some ofthese beams are indicated in FIG. 14C by arrows. The effect is that thespatial extent of the light is expanded since the input beam isreplicated as it propagates through the OPE region 1450. This is evidentfrom FIG. 14C, which shows that the input beam 1401 is replicated intomany light beams ultimately traveling generally in the −y-directiontoward the EPE region.

The EPE region 1460 likewise includes diffractive features which canperform at least two functions: first, they can replicate beams alonganother direction (e.g, a direction generally orthogonal to the one inwhich beams are replicated by the OPE region 1450); second, they candiffract each beam of light out of the eyepiece waveguide 1400 towardsthe user's eye. The EPE region 1460 can replicate light beams in thesame way as the OPE region 1450. Namely, as a beam propagates throughthe EPE region 1460, it repeatedly interacts with the diffractiongrating and portions of its power diffract into the first diffractiveorder, thereby being out-coupled toward the user's eye. Other portionsof the beam's power zero-order diffract and continue propagating in thesame direction within the EPE region 1460 until later interacting withthe grating again. The diffractive optical features of the EPE region1460 may also impart a degree of optical power to the replicated outputbeams of light to make them appear as if they originated from a desireddepth plane, as discussed elsewhere herein. This can be accomplished byimparting a curvature to the lines of the diffraction grating in the EPEregion 1460 using a lens function.

FIG. 14B illustrates the operation of the eyepiece waveguide 1400 ink-space. Specifically, FIG. 14B includes a k-space diagram (KSD) foreach component of the eyepiece waveguide 1400 to illustrate the k-spaceeffect of that component. The FOV rectangles in the k-space diagrams,and the arrows which show the corresponding directions of propagation oflight through the eyepiece waveguide, have matching shading. The firstk-space diagram, KSD1, shows the k-space representation of the inputbeams which are incident on the ICG region 1440 from an input device. Asalready discussed, the set of input beams can be represented in k-spaceby an FOV rectangle 1430 whose k_(x) and k_(y) dimensions correspond tothe angular spread of the input beams in the x- and y-directions. Eachspecific point in the FOV rectangle in KSD1 corresponds to the k-vectorassociated with one of the input beams, where the k_(x) component isindicative of the propagation angle of the input beam in the x-directionand the k_(y) component is indicative of the propagation angle of theinput beam in the y-direction. More precisely, k_(x)=sin(θ_(x)), whereθ_(x) is the angle formed by the input beam and the y-z plane, andk_(y)=sin(θ_(y)), where θ_(y) is the angle formed by the input beam andthe x-z plane. The fact that the FOV rectangle in KSD1 is centered onthe k_(z)-axis of the diagram means the represented input light beamshave propagation angles centered about an input beam propagating in the−z-direction and therefore all the input beams are propagating generallyin the −z-direction. (Although not illustrated here, any of thewaveguide displays described herein can also be designed for an FOV thatis off-axis with respect to the ±z-direction.)

The second k-space diagram, KSD2, shows the k-space operation of the ICGregion 1440. As already discussed, a diffraction grating has associatedgrating vectors (e.g., G₁, G⁻¹). KSD2 shows the G₁ grating vector andthe G⁻¹ grating vector, which are equal in magnitude and opposite indirection along the axis of periodicity of the ICG. The ICG region 1440diffracts the input beams into the ±1 diffractive orders. And, ink-space, this means that the ICG copies the FOV rectangle to two newlocations by translating it using both the G₁ and G⁻¹ grating vectors.In the illustrated instance, the ICG is designed with a period, A, basedon the angular frequency, ω, of the input beams such that the magnitudeof the grating vectors G₁, G⁻¹ places the copied FOV rectanglescompletely within the k-space annulus of the waveguide. Accordingly, allof the diffracted input beams enter guided propagation modes.

The copy of the FOV rectangle which is centered at a point on the−k_(x)-axis (9 o'clock position within the k-space annulus) indicatesthat the corresponding diffracted beams have propagation angles whichare centered around a beam whose propagation component in the plane ofthe eyepiece waveguide 1400 is in the −x-direction. Thus, all of thosebeams propagate generally toward the OPE region 1450, while reflectingback and forth between the front and back surfaces of the eyepiecewaveguide 1400 via TIR. Meanwhile, the copy of the FOV rectangle whichis centered at a point on the +k_(x)-axis (3 o'clock position within thek-space annulus) indicates that the corresponding diffracted beams havepropagation angles which are centered around a beam whose propagationcomponent in the plane of the eyepiece waveguide 1400 is in the+x-direction. Thus, all of those beams propagate generally toward theright edge of the eyepiece waveguide 1400, while reflecting back andforth between the front and back surfaces of the eyepiece waveguide 1400via TIR. In this particular eyepiece waveguide 1400, those beams aregenerally lost and do not meaningfully contribute to projection of theimage toward the eye of the user.

KSD2 does not illustrate the higher-order grating vectors, which aremultiples of the illustrated first-order grating vectors G₁, G⁻¹. TheICG does not diffract light beams into those diffractive orders becausedoing so in this instance would translate the k-vectors which make upthe FOV rectangle beyond the outer perimeter of the k-space disk whichdefines the permitted k-vectors. Accordingly, the higher diffractiveorders do not occur in this embodiment.

The third k-space diagram, KSD3, shows the k-space operation of the OPEregion 1450. Once again, since the OPE region 1450 includes adiffraction grating, it has associated grating vectors (e.g., G₁, G⁻¹)which are equal in magnitude and opposite in direction along the axis ofperiodicity of the OPE grating. In this case, the axis of periodicity ofthe diffraction grating is at a 45° angle with respect to the x-axis.Accordingly, the grating vectors (e.g., G₁, G⁻¹) of the OPE diffractiongrating point at 45° angles with respect to the k_(x)-axis. As shown inKSD3, one of the grating vectors translates the FOV rectangle to a newlocation centered at a point located on the −k_(y)-axis (6 o'clockposition within the k-space annulus). This copy of the FOV rectangleindicates that the corresponding diffracted beams have propagationangles which are centered around a beam whose propagation component inthe plane of the eyepiece waveguide 1400 is in the −y-direction towardthe EPE region 1460. Meanwhile, the other illustrated OPE grating vectorwould place the FOV rectangle at a location outside the outer perimeterof the k-space disk. But k-vectors outside the disk are not permitted,so the OPE diffraction grating does not diffract beams into thatdiffractive order. The axis of periodicity of the diffraction grating inthe OPE region 1450 need not necessarily be exactly 45°. For example, asseen by inspection of KSD3, the axis of periodicity could be at an anglesomewhat more or less than 45° while still translating the FOV rectangleto a 6 o'clock position where the FOV rectangle can fit entirely withinthe k-space annulus. This would place the FOV rectangle at a 6 o'clockposition but without the FOV rectangle necessarily being centered in thek-space annulus along the −k_(y)-axis.

In the illustrated instance, the OPE diffraction grating is designedwith a period, A, based on the angular frequency, ω, of the input beamssuch that one of the grating vectors G₁, G⁻¹ places the copied FOVrectangle completely within the k-space annulus of the waveguide at the6 o'clock position. Accordingly, all of the diffracted input beamsremain in guided propagating modes. Since the k-space distance from the9 o'clock position in the k-space annulus to the 6 o'clock position,which is the translation performed by the OPE grating, is greater thanthe distance from the origin of the k-space diagram to the annulus,which is the translation performed by the ICG, the OPE grating vectorsmust be different in magnitude than the ICG grating vectors. Inparticular, the OPE grating vectors are longer than the ICG gratingvectors, which means the OPE grating therefore has a shorter period, A,than the ICG grating.

The fourth k-space diagram, KSD4, shows the k-space operation of the EPEregion 1460. Again, since the EPE region 1460 includes a diffractiongrating, it has associated grating vectors (e.g., G₁, G⁻¹) which areequal in magnitude and opposite in direction along the axis ofperiodicity of the EPE grating. In this case, the axis of periodicity ofthe diffraction grating is along the y-axis of the eyepiece waveguide1400. Accordingly, the grating vectors (e.g., G₁, G⁻¹) of the EPEdiffraction grating point in the ±k_(y)-directions. As shown in KSD4,one of the grating vectors translates the FOV rectangle to a newlocation centered at the origin of the k-space diagram. This copy of theFOV rectangle indicates that the corresponding diffracted beams havepropagation angles which are centered around a beam whose propagationcomponent in the plane of the eyepiece waveguide 1400 is in the+z-direction toward the user's eye. Meanwhile, the other first order EPEgrating vector would place the FOV rectangle at a location outside theouter perimeter of the k-space disk, so the EPE diffraction grating doesnot diffract beams into that diffractive order. One of the second orderEPE grating vectors would, however, translate the FOV rectangle to the12 o'clock location in the k-space annulus. So, the EPE grating maydiffract some of the light into one of the second diffractive orders.The second order diffraction direction can correspond to guidedpropagation directions along the +y-direction, and is typically anundesirable effect. For example, the second order diffraction can resultin visual artifacts when the EPE grating is perturbed to introduceoptical power, as discussed below, resulting in a flare or smearingeffect in the image presented to the user.

In the illustrated instance, the EPE diffraction grating is designedwith a period, A, based on the angular frequency, ω, of the input beamssuch that one of the grating vectors G₁, G⁻¹ places the copied FOVrectangle completely within the inner k-space disk of the waveguide.Accordingly, all of the beams diffracted by the EPE diffraction gratingare no longer in guided propagation modes and therefore exit theeyepiece waveguide 1400. Moreover, since the EPE diffraction gratingtranslates the FOV rectangle back to the origin of the k-space diagram(where the FOV rectangle corresponding to the input beams was located),the output beams have the same propagation angles as their correspondinginput beams. In the illustrated embodiment, the EPE diffraction gratinghas the same period, A, as the ICG because both of these diffractiongratings translate the FOV rectangle by the same k-space distance. Thisis not a requirement, however. If the k_(y) dimension of the FOVrectangle is less than the k_(y) dimension of the k-space annulus in the6-o-clock position, then the FOV rectangle can have a range of possible6-o-clock positions at different k_(y) locations in the annulus. Hence,there may be numerous engineering choices for the EPE grating vector—andin turn the OPE vector—to place the FOV rectangle at locations withinthe k-space annulus and/or near the origin of the k-space diagram.

In some embodiments, the lines of the EPE diffraction grating may beslightly curved so as to impart optical power to the output beams whichexit the EPE region 1460. For example, the lines of the diffractiongrating in the EPE region 1460 can be bowed in the plane of thewaveguide toward the OPE region to impart negative optical power. Thiscan be used, for example, to make the output beams follow divergingpaths, as shown in FIG. 12B. This causes the projected image to appearat a depth plane nearer than optical infinity. The specific curvaturecan be determined by a lens function. In k-space, this means thatdifferent spatial regions within the EPE region 1460 will have gratingvectors that point in slightly different directions, depending on thecurvature of the grating lines in that specific region. In theseembodiments, this causes the FOV rectangle to be translated to a varietyof different locations centered around the origin of the k-spacediagram. This in turn causes the sets of output beams corresponding toeach of the translated FOV rectangles to be centered around differentpropagation angles, which in turn causes the illusion of depth.

FIG. 14D illustrates a technique for determining the sizes and shapes ofthe OPE region 1450 and the EPE region 1460. FIG. 14D illustrates thesame eyepiece waveguide 1400 shown in FIGS. 14A and 14B, including theICG region 1440, the OPE region 1450, and the EPE region 1460. FIG. 14Dalso includes simplified versions of the k-space diagrams KSD1, KSD2,and KSD3. With reference to the first k-space diagram, KSD1, the fourcorner k-vectors of the FOV rectangle are those which correspond to theinput beams which are incident on the ICG at the most oblique anglesfrom the corners of the image in the input plane (See FIGS. 12A and12B). Since the propagation angles of these input beams are the mostextreme of all those in the field of view, their k-vectors are locatedat the four corners of the FOV rectangle in k-space.

FIG. 14D shows rays which define the four diffracted beams from the ICGregion 1440 which correspond to the four corners of the input image. Inparticular, the ray near the top of the OPE region 1450 defines thediffracted beam corresponding to the input beam which is incident on theICG region 1440 at the most severe propagation angle in the directionupward and away from the OPE region (i.e., the k-vector located at thetop right corner of the FOV rectangle). And the ray near the bottom ofthe OPE region 1450 defines the diffracted beam corresponding to theinput beam which is incident on the ICG region 1450 at the most severepropagation angle downward and away from the OPE region (i.e., thek-vector located at the bottom right corner of the FOV rectangle). Thesetwo beams define the fan out of diffracted beams from the ICG region1440. In order to create replicated instances of these two beams, andall others in between, and project them toward the user's eye, the topand bottom boundaries of the OPE region should encompass the propagationpaths of these two beams. Their specific propagation paths can bedetermined with reference to the second k-space diagram, KSD2.

KSD2 shows the resulting k-vectors of the beams which diffract from theICG region 1440 toward the OPE region 1450. The arrow in KSD2 shows thepropagation angle of the beam corresponding to the k-vector located atthe top right corner of the FOV rectangle.

The size, shape, and location of the EPE region 1460 can be determinedby performing a backwards ray trace using the propagation angles whichare evident from the k-vectors in the third k-space diagram, KSD3. As isevident from KSD3, the top left and right corner k-vectors of the FOVrectangle define the fan out of the propagation paths which beams followwhile propagating in the direction from the OPE region 1450 toward theEPE region 1460. By using these propagation angles to trace backwardsfrom the portion of the EPE region 1460 which is located the furthestfrom the OPE region 1450 (i.e., the lower corners of the EPE region),one can determine the origination points in the OPE region of thoselight rays which would arrive at the lower corners of the EPE regionwith the propagation angles defined by the top left and right cornerk-vectors. These origination points of those rays can be used todetermine the remaining boundaries of the OPE region 1450. For example,to direct the beams from the OPE region 1450 to the lower left corner ofthe EPE region 1460, the worst-case propagation angle is the oneindicated by the top right corner k-vector of the FOV rectangle. Thus, apropagation path with that angle can be used to define the left boundaryof the OPE region 1450. Similarly, to direct the beams from the OPEregion 1450 to the lower right corner of the EPE region, the worst-casepropagation angle is the one indicated by the top left corner k-vectorof the FOV rectangle. Thus, a propagation path with that angle can beused to define the right boundary of the OPE region 1450.

As shown in FIG. 14D, in the case of the illustrated eyepiece waveguide1400, the EPE region 1460 is located in the −x and −y-directions fromthe ICG region 1440. And some of the diffracted beams fan out from theICG region 1440 along paths in those same directions. In order to avoidthese diffracted beams entering the EPE region before first havingpropagated through the OPE region 1450, the ICG region 1440 can belocated far enough away from the EPE region in the +y-direction suchthat the fan out of the diffracted beams does not intersect with the EPEregion 1460. This results in a gap between much of the lower border ofthe OPE region 1450 and the upper border of the EPE region 1460. In someembodiments, it may be desirable to decrease the size of the eyepiecewaveguide by removing or reducing this gap. FIG. 15A illustrates anexample embodiment which accomplishes these goals.

FIG. 15A illustrates an example embodiment of a waveguide eyepiece 1500in which the OPE region 1550 is tilted and located such that its lowerborder is parallel to the upper border of the EPE region 1560. In fact,the OPE region 1550 and the EPE region 1560 may actually share a border.According to this embodiment, the size of the waveguide eyepiece 1500can be made more compact by reducing or eliminating the gap between theOPE and EPE regions in the eyepiece waveguide embodiment shown in FIG.14A.

To accommodate the tilted orientation of the OPE region 1550, the ICGregion 1540 can be modified such that the fan out of diffracted beamsfrom the ICG region is tilted to match the tilted orientation of the OPEregion 1550. For example, the grating lines of the ICG region 1540 canbe oriented such that no diffracted beam exits the ICG region in apropagation direction that has a component in the −y-direction. Inaddition, the ICG region 1540 can be positioned near the shared borderof the OPE region 1550 and the EPE region 1560 but such that no portionof the ICG region extends in the −y-direction beyond that shared border.The operation of the ICG region 1540 can be seen in the k-space diagramsshown in FIG. 15B.

FIG. 15B includes k-space diagrams which illustrate the operation of theeyepiece waveguide 1500 shown in FIG. 15A. The first k-space diagram,KSD1, shows the FOV rectangle corresponding to the input beams which areprojected toward the ICG region 1540 from a projector located outsidethe eyepiece waveguide 1500. In the illustrated embodiment, these inputbeams have propagation angles centered about the −z-direction.Therefore, in k-space, they can be represented by an FOV rectanglecentered on the k_(z)-axis at the origin of KSD1.

The second k-space diagram, KSD2, shows the operation of the ICG region1540 on the input beams. The ICG region 1540 diffracts the input beamsand redirects them toward the OPE region 1550. In k-space, thiscorresponds to translating the FOV rectangle using the grating vector(s)associated with the ICG region 1540. In this embodiment, the gratinglines in the ICG region 1540 are oriented with an axis of periodicitywhich has a component in the +y-direction. This means that the gratingvector associated with the ICG 1540 also has a component in the+k_(y)-direction. The magnitude of this component in the+k_(y)-direction can be greater than or equal to one half of the widthof the FOV rectangle in the k_(y)-direction. This means that no portionof the FOV rectangle, after being translated by the ICG region 1540,extends below the horizontal axis of the k-space diagram KSD2. This inturn means that none of the diffracted beams from the ICG region 1540has a propagation angle with a component in the −k_(y)-direction.Accordingly, none of the diffracted beams travels downward toward theEPE region 1560 from the ICG region 1540. And, therefore, none of thediffracted beams will enter the EPE region 1560 prior to having passedthrough the OPE region 1550.

The third k-space diagram, KSD3, shows the operation of the OPE region1550 on the diffracted beams from the ICG region 1540. As illustrated,the diffraction grating of the OPE region 1550 can be oriented so as toredirect beams of light at angles which correspond to the FOV rectanglebeing translated to a position slightly displaced from the 6 o'clockposition in the k-space annulus. For example, the translated FOVrectangle in KSD3 can be displaced from the 6 o'clock position in thek-space annulus by the same angle as the translated FOV rectangle inKSD2 is displaced from the 9 o'clock position. In other words, thetranslated FOV rectangle in KSD3 can be separated by 90° from thetranslated FOV rectangle in KSD2. This specific angular separation isnot required, however; the specific location of each FOV rectangle canbe dependent upon the layout of the various regions of the eyepiecewaveguide with respect to one another.

Since the translated FOV rectangle in KSD3 is centered around a k-vectorwhich has a component in the −k_(x)-direction, the beams of light fromthe OPE region 1550 generally travel toward the EPE region 1560 atangles which have components in the −x-direction. It can be seen fromFIG. 15A that, due to this angle, some of the light beams from the tipportion 1555 of the OPE region 1550 will not intersect with the EPEregion 1560. Since the tip portion 1555 of the OPE region 1550 maycontribute a relatively small portion of light to the EPE region 1560,the size advantages of eliminating the upper tip 1555 may outweigh anyoptical disadvantages. In some embodiments, the waveguide eyepiece 1500can therefore be made even more compact by eliminating the upper tip1555 of the OPE region 1550.

Finally, the fourth k-space diagram, KSD4, shows that the EPE region1560 has a diffraction grating designed to translate the FOV rectangleback to the origin of the k-space diagram. Since the starting locationof the FOV rectangle in KSD4 for the eyepiece waveguide embodiment shownin FIG. 15A is slightly different from the starting location of the FOVrectangle in KSD4 for the eyepiece waveguide embodiment shown in FIG.14A, the design of the diffraction grating in the EPE region 1560 isalso somewhat different. For example, the orientation of the gratinglines of the diffraction grating in the EPE region 1560 can be tiltedsuch that the associated grating vector has a component in the+k_(x)-direction, so that the OPE region 1550 does not need to extendbeyond the left edge of the EPE region 1560 (see the discussion of FIG.14D and compare the location of the top right corner k-vector in KSD3 inFIG. 14D with the location of the corresponding k-vector in KSD3 in FIG.15B). This results in the FOV rectangle in KSD4 of FIG. 15B beingtranslated back to the origin of the k-space diagram, which means thebeams of light represented by the translated FOV rectangle are coupledout of the eyepiece waveguide 1500 toward the user's eye with the samepropagation angles as their corresponding input beams, as has alreadybeen described herein (i.e., the FOV rectangle which represents theoutput beams is in the same location on the k-space diagram as the FOVrectangle which represents the input beams).

FIG. 15C is another k-space diagram which illustrates the operation ofthe eyepiece waveguide 1500 shown in FIG. 15A. The k-space diagram inFIG. 15C is a superposition of all the k-space diagrams shown in FIG.15B. And it also illustrates that light beams propagating through theOPE region 1550 can switch back and forth between propagation anglesgenerally in the −k_(x)-direction (as represented by the FOV rectanglelocated near the 9 o'clock position of the k-space annulus) andpropagation angles generally in the −k_(y)-direction (as represented bythe FOV rectangle located near the 6 o'clock position of the k-spaceannulus). This is shown by the grating vector with the double-sidedarrow between the FOV rectangle near the 9 o'clock position of thek-space annulus and the FOV rectangle near the 6 o'clock position. FIGS.15D-15F illustrate this behavior in more detail.

FIG. 15D is a diagram of the first generation of interactions between aninput beam and the OPE region 1550 of the eyepiece waveguide embodimentshown in FIG. 15A. The OPE region 1550 of the eyepiece waveguide 1500includes a diffraction grating made up of parallel grating lines whichrepeat in a direction of periodicity. The direction of periodicitydetermines the direction of the grating vectors associated with thediffraction grating. In this instance, the grating vector with thedouble-sided arrow in FIG. 15C is the one which illustrates theoperation of the OPE region 1550 and which points along the direction ofperiodicity of the grating lines shown in FIGS. 15D-15F.

FIG. 15D shows an input beam that enters the OPE region 1550 from theICG region 1540. The input beam is shown propagating in the directionwhich corresponds to the center point, or k-vector, of the FOV rectanglelocated near the 9 o'clock position of the k-space annulus in FIG. 15C.As shown, the first generation of interactions between the input beamand the OPE region 1550 results in two diffracted output beams: someportion of the input beam's power simply reflects, as output₁, from thetop or bottom surface of the eyepiece waveguide 1500 and continues on inthe same x-y direction as the input beam (i.e., the 0^(th) orderdiffraction); and some portion of the input beam's power diffracts intothe first order (e.g., by the first order grating vector, G₁, of the OPEregion), downward as output₂. The output₂ beam is shown propagating inthe direction which corresponds to the center point, or k-vector, of theFOV rectangle located near the 6 o'clock position of the k-space annulusin FIG. 15C. After this first generation of interactions, the output₁beam and the output₂ beam have different propagation angles, but theyare both still propagating within the OPE region 1550 and may thereforehave additional interactions with the OPE region, as shown in FIGS. 15Eand 15F. Although not illustrated, other input beams that enter the OPEregion 1550 with different propagation angles will behave similarly butwith slightly different input and output angles.

FIG. 15E is a diagram of the second generation of interactions betweenan input beam and the OPE region 1550 of the eyepiece waveguideembodiment shown in FIG. 15A. The beams related to the first generationof interactions are shown with dashed lines, while the beams related tothe second generation of interactions are shown with solid lines. Asshown in FIG. 15E, each of the output beams, output₁ and output₂, fromthe first generation of interactions can now undergo similarinteractions with the OPE region 1550 as occurred in the firstgeneration. Namely, some portion of the power from the output₁ beam fromFIG. 15D simply continues on in the same x-y direction (i.e., the 0^(th)order diffraction), while another portion of the power of that beaminteracts with the grating and is redirected downward (e.g., by thefirst order grating vector, G₁, of the OPE region). Similarly, someportion of the power from the output₂ beam from FIG. 15D simplycontinues downward toward the EPE region 1560 (i.e., the 0^(th) orderdiffraction), while another portion of the power of that beam interactswith the grating and is diffracted (e.g., by the negative first ordergrating vector, G⁻¹, of the OPE region), generally in the −x-direction,and continues propagating further into the OPE region 1550 in the samedirection as the initial input beam.

After the second generation of interactions have occurred within the OPEregion 1550, there is an interference node 1556 where two of theresulting beams intersect. The optical paths followed by each of thesebeams to arrive at the interference node 1556 are substantiallyidentical in length. Thus, the beams which leave the interference node1556 propagating in the same direction may have the same or similarphases and may therefore undergo constructive or destructive waveinterference with one another. This can result in image artifacts whichare discussed below.

FIG. 15F is a diagram of the third generation of interactions between aninput beam and the OPE region 1550 of the eyepiece waveguide embodimentshown in FIG. 15A. The beams related to the first and second generationsof interactions are shown with dashed lines, while the beams related tothe third generation of interactions are shown with solid lines. Asshown in FIG. 15F, each of the output beams which resulted from thesecond generation of interactions can once more experience similarinteractions with the OPE region 1550 as occurred in previousgenerations. Some portions of the power of those beams continue on inthe same direction (i.e., the 0^(th) order diffraction), while otherportions of the power of those beams are redirected—some generally inthe −x-direction and some generally in the −y-direction (i.e., by thefirst order grating vectors, G₁ and G⁻¹, of the OPE region). All of thebeams propagating generally in the −x-direction are in the staterepresented by the FOV rectangle located near the 9 o'clock position inthe k-space annulus of the k-space diagram in FIG. 15C, while all of thebeams propagating generally in the −y-direction are in the staterepresented by the FOV rectangle located near the 6 o'clock position. Ascan be seen in FIG. 15C, for the case of an OPE region 1550 made up of a1D periodicity diffraction grating, for any given input beam, thereplicated beams of light corresponding to that input beam only travelin two directions within the OPE region (although the two directionswill be different for different input beams which enter the OPE regionat different propagation angles).

The third generation of interactions with the OPE region results in thecreation of additional interference nodes 1556 where beams with the sameor similar optical path lengths intersect with one another, possiblyresulting in constructive or destructive wave interference. Each of thenodes 1556 serves as a source of light emitted toward the EPE region1560. In the case of an OPE region made up of a diffraction grating with1D periodicity, the layout of these nodes 1556 forms a uniform latticepattern and can therefore result in image artifacts, as shown in FIG.15G.

FIG. 15G is a diagram which illustrates how a single input beam 1545from the ICG region 1540 is replicated by the OPE region 1550 andredirected toward the EPE region 1560 as a plurality of beams 1565. Eachof the replicated beams 1565 shown propagating toward, or in, the EPEregion 1560 originates from one of the interference nodes 1556. Theseinterference nodes have an ordered distribution and serve as a sparse,periodic array of sources. Due to the ordered distribution of theinterference nodes 1556, the replicated beams 1565 which illuminate theEPE region are all separated by the same spacing, although the beams mayhave non-monotonically varying intensity. And as a result, thereplicated light beams 1565 from the OPE region 1550 may illuminate theEPE region 1560 with a relatively sparse, uneven distribution. In someembodiments, it may be advantageous if the replicated light beams whichilluminate the EPE region of an eyepiece waveguide could be more evenlydispersed. FIG. 16 illustrates such an embodiment.

Example AR Eyepiece Waveguides with Multi-Directional Pupil Expanders

FIG. 16A illustrates an example eyepiece waveguide 1600 that has amulti-directional pupil expander (MPE) region 1650 rather than an OPEregion. On a macroscopic level, the illustrated embodiment of theeyepiece waveguide 1600 is similar to the eyepiece waveguide 1500 shownin FIG. 15A. Input beams are coupled into the eyepiece waveguide 1600 bythe ICG region 1640. The diffracted beams from the ICG region 1640propagate toward and through the MPE region 1650, which takes the placeof an OPE region. Finally, the MPE region 1650 diffracts beams of lighttoward the EPE region 1660, where they are out coupled toward the user'seye. The ICG region 1640 and the EPE region 1660 may be designed tofunction in the same way as the corresponding regions in the eyepiecewaveguide 1500 described with respect to FIGS. 15A-15G. The MPE region1650, however, is distinct from the OPE region 1550 in that it diffractslight in more directions. This feature can advantageously decrease theperiodic uniformity in the distribution of light beams in the EPE region1660, which in turn can cause the EPE region to be illuminated moreevenly.

The MPE region 1650 is made up of diffractive features which exhibitperiodicity in multiple directions. The MPE region 1650 may be composedof an array of scattering features arranged in a 2D lattice. Theindividual scattering features can be, for example, indentations orprotrusions of any shape. The 2D array of scattering features hasassociated grating vectors, which are derived from the reciprocallattice of that 2D lattice. As one example, the MPE region 1650 could bea 2D periodic diffraction grating composed of a crossed grating withgrating lines that repeat along two or more distinct directions ofperiodicity. This can be accomplished by superimposing two 1D gratingswith different directions of periodicity.

FIG. 16B illustrates a portion of an example 2D periodic grating, alongwith its associated grating vectors, which can be used in the MPE region1650 shown in FIG. 16A. The 2D periodic grating 1650 can be a spatiallattice of diffractive features whose directions of periodicity areillustrated by the vectors u and v. Such a 2D periodic grating isassociated with grating vectors. The two fundamental grating vectors, Gand H, corresponding to the directions of periodicity, u and v, aremathematically defined by:

u = ⌊u_(x), u_(y)⌋ v = ⌊v_(x), v_(y)⌋$G = {\frac{2\; \pi}{{u_{x}v_{y}} - {u_{y}v_{x}}}\left\lfloor {v_{y},{- v_{x}}} \right\rfloor}$$H = {\frac{2\; \pi}{{u_{x}v_{y}} - {u_{y}v_{x}}}\left\lfloor {{- u_{y}},u_{x}} \right\rfloor}$

Mathematically, the vectors u and v define a spatial lattice, and G andH correspond to the fundamental dual, or reciprocal, lattice vectors.Note, that G is orthogonal to u, and H is orthogonal to v; however, u isnot necessarily parallel to H, and v is not necessarily parallel to G.

As one example, the 2D periodic grating can be designed or formed bysuperimposing two sets of 1D periodic grating lines, as shown in FIG.16B (though the 2D periodic grating could instead be made up ofindividual scattering features located at, for example, the intersectionpoints of the grating lines shown in FIG. 16B). The first set of gratinglines 1656 can repeat along the direction of the fundamental gratingvector G. The fundamental grating vector G can have a magnitude equal to2π/a, where a is the period of the first set of grating lines 1656. The2D grating shown in FIG. 16B is also associated with harmonics of thefirst fundamental grating vector G. These include −G and higher-orderharmonics, such as 2G, −2G, etc. The second set of grating lines 1657can repeat along the direction of the fundamental grating vector H. Thefundamental grating vector H can have a magnitude equal to 2π/b, where bis the period of the second set of grating lines 1657. The 2D gratingshown in FIG. 16B is also associated with harmonics of the secondfundamental grating vector H. These include −H and higher-orderharmonics, such as 2H, −2H, etc.

Any 2D periodic array of diffractive features will have associatedgrating vectors which correspond to the entire reciprocal lattice andpoint in directions determined by integer linear combinations(superpositions) of the basis grating vectors, G and H. In theillustrated embodiment, these superpositions result in additionalgrating vectors which are also shown in FIG. 16B. These include, forexample, −G, −H, H+G, H−G, G−H, and −(H+G). Typically, these vectors aredescribed with two indices: (±1,0), (0, ±1), (±1, ±1), (±2,0), etc.Although FIG. 16B only illustrates the first order grating vectors, andtheir superpositions, associated with the 2D diffraction grating,higher-order grating vectors may also exist.

As already discussed elsewhere herein, the k-space operation of agrating on a set of light beams composing an image is to translate theFOV rectangle corresponding to the image using the grating vectorsassociated with the grating. This is shown in FIGS. 16C and 16D for theexample 2D MPE diffraction grating shown in FIG. 16B.

FIG. 16C is a k-space diagram which illustrates the k-space operation ofthe MPE region 1650 of the eyepiece waveguide 1600 shown in FIG. 16A.The k-space diagram includes a shaded FOV rectangle located near the 9o'clock position of the k-space annulus. This is the location of the FOVrectangle after the ICG region 1640 has coupled the input beams into theeyepiece waveguide 1600 and redirected them toward the MPE region 1650.FIG. 16C shows how the 2D grating in the MPE region 1650 translates theFOV rectangle using the grating vectors shown in FIG. 16B. Since thereare eight grating vectors (G, H, −G, −H, H+G, H−G, G−H, and −(H+G)), theMPE region 1650 attempts to translate the FOV rectangle to eightpossible new k-space locations. Of these eight possible k-spacelocations, six fall outside the outer periphery of the k-space diagram.These are illustrated with unshaded FOV rectangles. Since k-vectorsoutside the bounds of the k-space diagram are not permitted, none ofthose six grating vectors results in diffraction. There are, however,two grating vectors (i.e., −G and −(H+G)) which do result intranslations of the FOV rectangle to new positions within the bounds ofthe k-space diagram. One of these locations is near the 6 o'clockposition in the k-space annulus, and the other is near the 2 o'clockposition. Since k-vectors at these locations are permitted and do resultin guided propagation modes, the FOV rectangles at these locations areshaded to indicate that beams of light are diffracted into those twostates. Thus, the power of beams of light entering the MPE region 1650with the propagation angles indicated by the FOV rectangle located nearthe 9 o'clock position of the k-space annulus is partially diffractedinto both of the states indicated by the other two shaded FOV rectangles(i.e., the FOV rectangle near the 2 o'clock position and the FOVrectangle near the 6 o'clock position).

FIG. 16D is a k-space diagram which further illustrates the k-spaceoperation of the MPE region 1650 of the eyepiece waveguide 1600 shown inFIG. 16A. This particular k-space diagram illustrates the operation ofthe MPE region 1650 on beams of light which are in the propagation stateillustrated by the FOV rectangle located near the 2 o'clock position ofthe k-space annulus. Once again, the 2D diffraction grating in the MPEregion 1650 attempts to diffract these beams of light into diffractiveorders specified by its eight associated grating vectors. As shown, sixof the grating vectors would translate the FOV rectangle to a positionoutside the bounds of the k-space diagram. Thus, those diffractiveorders do not occur. These positions are illustrated with unshaded FOVrectangles. However, two of the grating vectors (i.e., H and H−G)translate the FOV rectangle to positions within the bounds of thek-space diagram. These are illustrated by the shaded FOV rectangleslocated near the 9 o'clock position of the k-space annulus and near the6 o'clock position. Thus, the 2D diffraction grating in the MPE region1650 partially diffracts the power of beams propagating in thedirections indicated by the FOV rectangle located near the 2 o'clockposition of the k-space annulus into both of the states indicated by theother two shaded FOV rectangles (i.e., the FOV rectangle near the 9o'clock position and the FOV rectangle near the 6 o'clock position).

Although not illustrated, a similar k-space diagram could be drawn toillustrate the k-space operation of the MPE region 1650 on beams oflight traveling with the propagation angles indicated by the FOVrectangle located near the 6 o'clock position of the k-space annulus.That k-space diagram would show that the 2D period diffraction gratingin the MPE region 1650 partially diffracts the power of those beams intoboth of the states indicated by the two shaded FOV rectangles locatednear the 9 o'clock position and near the 2 o'clock position of thek-space annulus.

FIG. 16E is a k-space diagram which illustrates the k-space operation ofthe eyepiece waveguide 1600 shown in FIG. 16A. As already mentioned, theeyepiece waveguide 1600 can receive input beams of light which propagategenerally in the −z-direction and are incident on the ICG region 1640 ofthe waveguide 1600 from an outside source. Those input beams arerepresented by the FOV rectangle centered on the k_(z)-axis at theorigin of the k-space diagram. The ICG region 1640 then diffracts theinput beams such that they are guided and have propagation anglescentered around a propagation direction which corresponds to the centerpoint of the FOV rectangle located near the 9 o'clock position of thek-space annulus.

The guided beams enter the MPE region 1650, where they can have multipleinteractions. During each generation of interactions, a portion of thepower of each of the beams can zero-order diffract and continuepropagating in the same direction through the MPE region 1650. In thefirst generation of interactions, for example, this zero-orderdiffraction corresponds to that portion of the power of those beamsstaying in the state indicated by the FOV rectangle located near the 9o'clock position of the k-space annulus. Other portions of the power ofthe beams can be diffracted in new directions. Again, in the firstgeneration of interactions, this creates respective diffracted beamsthat have propagation angles centered around a propagation directionwhich corresponds to the center point of the FOV rectangle located nearthe 2 o'clock position of the k-space annulus and a propagationdirection which corresponds to the center point of the FOV rectanglelocated near the 6 o'clock position.

So long as the beams remain in the MPE region 1650, they can experienceadditional interactions, each of which results in portions of the powerof the beams zero-order diffracting and continuing on in the samedirection, or being diffracted in new directions. This results inspatially distributed sets of diffracted beams that have propagationangles centered around each of the propagation directions indicated bythe center points of the FOV rectangles in the k-space annulus shown inFIG. 16E. This behavior is represented by the double-sided arrowsbetween each pair of FOV rectangles in the k-space annulus.

As any given input beam of light propagates within the MPE region 1650,it is split into many diffracted beams which can only travel in threeallowed directions—each direction being defined by the correspondingk-vector, or point, within the FOV rectangles in the annulus of thek-space diagram in FIG. 16E. (This is true for any input beam of lightpropagating within the MPE region 1650. However, the three alloweddirections will be slightly different depending on the propagation angleat which each initial input beam enters the MPE region 1650.) And sinceportions of the power of any given input beam of light are diffractedinto any of the same three propagation directions after any number ofinteractions with the MPE region 1650, image information is preservedthroughout these interactions.

There are advantages associated with the MPE region 1650 having threepermissible propagation directions for each input beam—as opposed to thetwo permissible propagation directions of the OPE region 1550. Theseadvantages are discussed further below, but suffice it to say for nowthat the increased number of propagation directions in the MPE region1650 can result in a more complicated distribution of interference nodeswithin the MPE region 1650, which can in turn improve the evenness ofillumination in the EPE region 1660.

It should be understood that FIG. 16E illustrates the k-space operationof one example embodiment of the MPE region 1650. In other embodiments,the MPE region 1650 can be designed such that each input beam of lightcan diffract in more than three directions within the MPE region. Forexample, in some embodiments the MPE region 1650 may be designed toallow diffraction of each input beam of light in 4 directions, 5directions, 6 directions, 7 directions, 8 directions, etc. As alreadydiscussed, the diffractive features in the MPE region 1650 can bedesigned to provide grating vectors which copy the FOV rectangle tolocations in the k-space annulus corresponding to the selecteddiffraction directions. In addition, the diffractive features in the MPEregion 1650 can be designed with periods corresponding to grating vectormagnitudes which result in these copies of the FOV rectangle lyingentirely inside the k-space annulus (and such that other attemptedcopies of the FOV rectangle lie entirely outside the outer periphery ofthe k-space diagram).

In some embodiments, the angular separation between each of thepermitted propagation directions for a given beam of light inside theMPE region 1650 is at least 45 degrees. If the angular separationbetween any pair of the selected directions is less than this amount,then the diffractive features in the MPE region 1650 would need to bedesigned to provide grating vectors to make those angular transitions inthe k-space annulus; and such grating vectors would be relatively shortin comparison to the size of the k-space annulus due to the lesserangular separation. This could make it more likely that superpositionsof the fundamental MPE grating vectors would create copies of the FOVrectangle which lie only partially inside the k-space annulus, which mayresult in the loss of image information (if not done carefully, asdiscussed further herein). In addition, if the angular separationbetween any pair of permitted propagation directions in the MPE region1650 becomes too small, then the resulting relatively short gratingvectors could also make it more likely that grating vectorsuperpositions would create copies of the FOV rectangle which liepartially inside the central disk of the k-space diagram. This could beundesirable because it could result in light being out-coupled from theeyepiece waveguide 1600, toward the user's eye, from a location outsidethe designated EPE region 1660.

Various design guidelines can be followed when determining thepermissible propagation directions within the MPE region 1650. Forexample, the permissible propagation directions can be selected suchthat one corresponds to the direction from the ICG region 1640 to theMPE region 1650. In addition, the permissible propagation directions canbe selected such that only one would cause beams of light whichpropagate in that direction from a location inside the MPE region 1650to intersect with the EPE region 1660. This ensures that the replicatedbeams of light which correspond to each input beam enter the EPE region1660 with the same propagation angle. In addition, the permissiblepropagation directions inside the MPE region 1650 can be selected suchthat the FOV rectangles do not overlap. Overlapping of FOV rectanglescan result in mixing of image information from different image pointsand can cause ghost images.

FIG. 16F is a diagram of the first generation of interactions between aninput beam and the MPE region 1650 of the eyepiece waveguide embodimentshown in FIG. 16A. FIG. 16F shows an input beam that enters the MPEregion 1650 from the ICG region 1640. The input beam is shownpropagating in the direction which corresponds to the center point, ork-vector, of the FOV rectangle located near the 9 o'clock position ofthe k-space annulus in FIG. 16E.

The MPE region 1650 can include many sub-1 μm features. And at everyinteraction with the MPE region, an input ˜1 mm-diameter beam will splitinto 3 beams (with the same diameter but a fraction of the originalpower of the input beam) propagating in 3 different directions in TIR.One direction corresponds to zero-order diffraction and is the originalpropagation angle in the plane of the waveguide. The other twodirections depend on the grating vectors G and H of the MPE region 1650.As shown, the first generation of interactions between the input beamand the MPE region 1650 results in three beams: some portion of thepower of the input beam simply reflects, as output₁, from the top orbottom surface of the eyepiece waveguide 1600 and continues on in thesame x-y direction as the input beam (i.e., the 0^(th) orderdiffraction); some portion of the power of the input beam interacts withthe 2D grating in the MPE region 1650 and is diffracted downward asoutput₂; and some portion of the power of the input beam interacts withthe grating and is diffracted upward and to the right as output₃. Theoutput₂ beam is shown propagating in the direction which corresponds tothe center point, or k-vector, of the FOV rectangle located near the 6o'clock position of the k-space annulus in FIG. 16E, while the output₃beam is shown propagating in the direction which corresponds to thecenter point, or k-vector, of the FOV rectangle located near the 2o'clock position. After this first generation of interactions, theoutput₁ beam, the output₂ beam, and the output₃ beam have differentpropagation angles, but they are all still propagating within the MPEregion 1650 and may therefore have additional interactions with the MPEregion, as shown in FIGS. 16G-16I. Although not illustrated, other inputbeams that enter the MPE region 1650 with different propagation angleswill behave similarly but with slightly different input and outputangles.

FIG. 16G is a diagram of the second generation of interactions betweenan input beam and the MPE region 1650 of the eyepiece waveguideembodiment shown in FIG. 16A. The beams related to the first generationof interactions are shown with dashed lines, while the beams related tothe second generation of interactions are shown with solid lines. Asshown in FIG. 16G, each of the output beams, output₁, output₂, andoutput₃, from the first generation of interactions can now undergosimilar interactions with the MPE region 1650 as occurred in theprevious generation. Namely, some portion of the power of the output₁beam from FIG. 16F simply continues on in the same x-y direction, whileanother portion of the power of that beam interacts with the grating andis diffracted in the direction corresponding to the FOV rectanglelocated near the 6 o'clock position, and still another portion of thepower of that beam interacts with the grating and is diffracted in thedirection corresponding to the FOV rectangle located near the 2 o'clockposition. Similarly, some portion of the power of the output₂ beam fromFIG. 16F simply continues toward the EPE region 1660, while anotherportion of the power of that beam interacts with the grating and isdiffracted in the direction indicated by the FOV rectangle located nearthe 9 o'clock position, and still another portion of the power of thatbeam interacts with the grating and is diffracted in the directioncorresponding to the FOV rectangle located near the 2 o'clock position.Further, some portion of the power of the output₃ beam from FIG. 16Fsimply continues in the direction indicated by the FOV rectangle locatednear the 2 o'clock position, while another portion of the power of thatbeam interacts with the grating and is diffracted in the directionindicated by the FOV rectangle located near the 9 o'clock position, andstill another portion of the power of that beam interacts with thegrating and is diffracted in the direction corresponding to the FOVrectangle located near the 6 o'clock position.

FIG. 16H is a diagram of the third generation of interactions between aninput beam and the MPE region 1650 of the eyepiece waveguide embodimentshown in FIG. 16A. The beams related to the first and second generationsof interactions are shown with dashed lines, while the beams related tothe third generation of interactions are shown with solid lines. Asshown in FIG. 16H, each of the output beams which resulted from thesecond generation of interactions can once more experience similarinteractions with the MPE region 1650 as occurred in the previousgenerations.

FIG. 16I is a diagram of the fourth generation of interactions betweenan input beam and the MPE region 1650 of the eyepiece waveguideembodiment shown in FIG. 16A. The beams related to the first, second,and third generations of interactions are shown with dashed lines, whilethe beams related to the fourth generation of interactions are shownwith solid lines. After all these interactions, all of the resultingbeams are propagating in one of the three directions which are permittedinside the MPE region 1650 for any given input beam: the directioncorresponding to the FOV rectangle located near the 9 o'clock position;the direction corresponding to the FOV rectangle located near the 2o'clock position; or the direction corresponding to the FOV rectanglelocated near the 6 o'clock position of the k-space annulus. Althoughthere are nodes where some of these beams may intersect with one anotherwhile propagating through the MPE region 1650, the locations of thosenodes have a more complex distribution than in the case of the OPEregion 1550 which was illustrated in FIGS. 15D-15G. Further, beams canarrive at each of these nodes via different paths and therefore will notnecessarily be in phase with one another. Accordingly, image artifactswhich may result from the ordered distribution of interference nodes canbe reduced in the eyepiece waveguide embodiment 1600 which uses an MPEregion 1650 instead of an OPE region (e.g., 1550). This can be seen inFIGS. 16J and 16K.

FIG. 16J is a diagram which illustrates various paths which beams mayfollow through the MPE region 1650 and ultimately to the EPE region1660. There are some paths which only include a single change indirection, while others include multiple changes in direction (thoughsome of the longer, more complicated pathways will naturally carry lesspower). Due to the complexity introduced by the existence of anotherdiffraction angle in the MPE region 1650, there are many differentspacings between the beams of light 1665 which ultimately illuminate theEPE region 1660. And, in fact, any possible spacing between the lightbeams 1665 can be achieved through a sufficient number of interactionsin the MPE region 1650. As shown in FIG. 16K, this can result in moreeven illumination of the EPE region 1660.

FIG. 16K is a diagram which illustrates how a single input beam 1645from the ICG region 1640 is replicated by the MPE region 1650 andredirected toward the EPE region 1660 as a plurality of beams 1665. Eachof these beams 1665 originates from a dense grid of nodes. There maystill be gaps between some of these replicated beams 1665, but they aregenerally smaller and less regular than the gaps between the replicatedbeams which are output from an OPE region (e.g., 1550, as shown in FIG.15G). Since there are so many pathways toward the EPE region 1660, allat different positions, the MPE region 1650 provides a complex exitpupil pattern which can more evenly illuminate the EPE region 1560.

FIG. 16L is a side-by-side comparison which illustrates the performanceof an eyepiece waveguide with an OPE region versus that of an eyepiecewaveguide with an MPE region. On the left is shown the eyepiecewaveguide 1500, which includes an OPE region 1550 with a 1D periodicdiffraction grating. As already discussed, the OPE region 1550illuminates the EPE region 1560 with a sparse set of regularly spacedreplicated light beams. Below the eyepiece waveguide 1500 is a simulatedoutput image. This is the simulated output image which would beprojected from the EPE region 1560 of the eyepiece waveguide 1500 inresponse to an input image made up of pixels that all have the samecolor and brightness.

On the right, FIG. 16L shows the eyepiece waveguide 1600 which includesan MPE region 1650 with a 2D periodic diffraction grating. As can beseen in the figure, the MPE region 1650 illuminates the EPE region 1660more evenly. Below the eyepiece waveguide 1600 is a simulated outputimage which is the result of the same input image used in the simulationfor the eyepiece waveguide 1500 on the left. It is clear from thesimulated image on the right that the eyepiece waveguide 1600 that usesthe MPE region 1650 achieves a smoother, more uniform distribution ofoutput light. In contrast, the image on the left, which is the simulatedoutput of the eyepiece waveguide 1500 with the OPE region 1550, hasvisible high spatial frequency striations which result from the sparse,ordered set of replicated light beams which illuminate its EPE region1560.

FIG. 16M further illustrates the performance of an eyepiece waveguidewith an MPE region versus others with OPE regions. The top row of graphsin FIG. 16M illustrate the performance of the eyepiece waveguide 1500shown in FIG. 15A. The graph of the horizontal cross-section of aprojected image from this eyepiece waveguide shows the relatively highspatial frequency variation which was visible as striations in thesimulated output image shown in FIG. 16L. FIG. 16M shows that theeyepiece waveguide 1500 has an eyebox efficiency of 1.2%. It also showsthe point spread function associated with this eyepiece waveguide. Thepoint spread function illustrates the output image obtained from theeyepiece waveguide in response to an input image of a single brightpoint. This shows that the eyepiece waveguide 1500 is quite sharp, as itonly has blur of 2.5-5 arc minutes.

One approach to overcoming the high spatial frequency variation inoutput images from the eyepiece waveguide 1500 is to introduce somedithering in the OPE region 1550. For example, small variations can beintroduced in the orientation angle and/or grating period of the OPEregion 1550. This is done in an attempt to disrupt the ordered nature ofthe interference nodes which can be present in the OPE region 1550. Thesecond and third rows in FIG. 16M illustrate the performance of theeyepiece waveguide 1500 with two different types of dithering. As can beseen in the horizontal cross-sections of the projected images for thesewaveguides, the high spatial frequency variations are still present.Further, the point spread functions for these dithered embodiments showa much larger amount of blur—in one case as much as 45 arc minutes.

The bottom row of FIG. 16M illustrates the performance of the eyepiecewaveguide 1600 with an MPE region 1650. The cross-section of theprojected image for this waveguide shows much less high spatialfrequency variation. While there is still low frequency spatialvariation, this can be corrected via software much more easily than canhigh spatial frequency variation. The eyebox efficiency of this eyepiecewaveguide is slightly less, at 0.9%, than the others. This can beattributed to the fact that the MPE region 1650 redirects some of theinput light in a general direction corresponding to the FOV rectanglelocated near the 2 o'clock position in the annulus of the k-spacediagram shown in FIG. 16E. Due to the macroscopic layout of the eyepiecewaveguide 1600, light which exits the MPE region 1650 with thispropagation direction never enters the EPE region and is therefore notprojected toward the user's eye; instead, it is lost out the edge of thewaveguide 1600. However, this loss of light results in only a relativelysmall decrease in eyebox efficiency. Meanwhile, the point spreadfunction for the eyepiece waveguide 1600 shows that it is quite sharp,with a blur of only 2.5-5 arc minutes.

FIGS. 16A-16M illustrate an eyepiece waveguide 1600 with an MPE region1650 that has three permissible propagation directions for each inputbeam. However, other embodiments of MPE regions can be designed to alloweven more propagation directions for each input beam. One such exampleis illustrated in FIGS. 17A-17G. These figures illustrate an eyepiecewaveguide 1700 that is identical in its macroscopic design to theeyepiece waveguide 1600. Namely, the eyepiece waveguide 1700 includes anICG region 1740, an MPE region 1750, and an EPE region 1760 which areall arranged in the same way as the corresponding regions in theeyepiece waveguide 1600 shown in FIG. 16A. However, the eyepiecewaveguide 1700 differs in the microscopic design of its MPE region 1750.

FIG. 17A illustrates a portion of an example 2D grating, along with itsassociated grating vectors, which can be used in the MPE region 1750 ofthe eyepiece waveguide 1700. The 2D periodic grating 1750 can be aspatial lattice of diffractive features whose directions of periodicityare u and v. As already discussed, such a 2D periodic grating isassociated with fundamental grating vectors, G and H. As one example,the 2D periodic grating 1750 can be designed or formed by superimposingtwo sets of 1D periodic grating lines (though the 2D periodic gratingcould instead be made up of individual scattering features located at,for example, the intersection points of the grating lines shown in FIG.17A). The first set of grating lines 1756 can repeat along the directionof the fundamental grating vector G. The fundamental grating vector Gcan have a magnitude equal to 2π/a, where a is the period of the firstset of grating lines 1756. The 2D grating shown in FIG. 17B is alsoassociated with harmonics of the first fundamental grating vector G.These include −G and higher-order harmonics, such as 2G, −2G, etc. Thesecond set of grating lines 1757 can repeat along the direction of thefundamental grating vector H. The fundamental grating vector H can havea magnitude equal to 2π/b, where b is the period of the second set ofgrating lines 1657. The 2D grating shown in FIG. 17B is also associatedwith harmonics of the second fundamental grating vector H. These include−H and higher-order harmonics, such as 2H, −2H, etc. And, as alreadydiscussed, any 2D periodic array of diffractive features will haveassociated grating vectors which point in directions determined byinteger linear combinations (superpositions) of the fundamental gratingvectors. In this case, these superpositions result in additional gratingvectors. These include, for example, −G, −H, H+G, H−G, G−H, and −(H+G).Although FIG. 17A only illustrates the first order grating vectors, andtheir superpositions, associated with the 2D diffraction grating,higher-order grating vectors may also exist.

FIG. 17B is a k-space diagram which illustrates the k-space operation ofthe MPE region 1750 of the eyepiece waveguide 1700. The k-space diagramincludes a shaded FOV rectangle located near the 9 o'clock position ofthe k-space annulus. This is the location of the FOV rectangle after theICG region 1740 has coupled the input beams into the eyepiece waveguide1700 and redirected them toward the MPE region 1750. FIG. 17B shows howthe 2D grating in the MPE region 1750 translates the FOV rectangle usingthe grating vectors shown in FIG. 17A. Since there are eight gratingvectors, the MPE region 1750 attempts to translate the FOV rectangle toeight possible new locations in the k-space diagram. Of these eightpossible locations, five fall outside the outer periphery of the k-spacediagram. These locations are illustrated with unshaded FOV rectangles.Since k-vectors outside the outer periphery of the k-space diagram arenot permitted, none of those five grating vectors results indiffraction. There are, however, three grating vectors (i.e., −H, −G,and −(H+G)) which do result in translations of the FOV rectangle to newpositions within the bounds of the k-space diagram. One of theselocations is near the 6 o'clock position in the k-space annulus, anotheris near the 12 o'clock position, and the last is near the 3 o'clockposition. Since k-vectors at these locations are permitted and do resultin guided propagation modes, the FOV rectangles at these locations areshaded to indicate that beams of light are diffracted into those threestates. Thus, beams of light entering the MPE region 1750 with thepropagation angles indicated by the FOV rectangle located near the 9o'clock position of the k-space annulus are diffracted into all of thestates indicated by the other three shaded FOV rectangles (i.e., the FOVrectangle near the 12 o'clock position, the FOV rectangle near the 3o'clock position, and the FOV rectangle near the 6 o'clock position).

Although not illustrated, similar k-space diagrams could be drawn toillustrate the k-space operation of the MPE region 1750 on beams oflight traveling with the propagation angles indicated by the FOVrectangles located near the 12 o'clock position, near the 3 o'clockposition, and near the 6 o'clock position of the k-space annulus. Thosek-space diagrams would show that the 2D diffraction grating in the MPEregion 1750 diffracts those beams into all of the remaining statesindicated by the shaded FOV rectangles in the annulus of the k-spacediagram in FIG. 17B.

FIG. 17C is a k-space diagram which illustrates the k-space operation ofthe eyepiece waveguide 1700. The eyepiece waveguide 1700 can receiveinput beams of light which propagate generally in the −z-direction andare incident on an ICG region 1740 of the waveguide 1700 from an outsidesource. Those input beams are represented by the FOV rectangle centeredon the k_(z)-axis at the origin of the k-space diagram. The ICG region1740 then diffracts the input beams such that they are guided and havepropagation angles centered around a propagation direction whichcorresponds to the center point of the FOV rectangle located near the 9o'clock position of the k-space annulus.

The diffracted beams enter the MPE region 1750, where they can havemultiple interactions. During each generation of interactions, a portionof the power of each of the beams continues propagating in the samedirection through the MPE region 1750. In the first generation ofinteractions, for example, this would correspond to that portion of thepower of those beams staying in the state indicated by the FOV rectanglelocated near the 9 o'clock position. Other portions of the power of thebeams can be diffracted in new directions. Again, in the firstgeneration of interactions, this creates respective diffracted beamsthat have propagation angles centered around a propagation directionwhich corresponds to the center point of the FOV rectangle located nearthe 12 o'clock position of the k-space annulus, the center point of theFOV rectangle located near the 3 o'clock position, and the center pointof the FOV rectangle located near the 6 o'clock position.

The diffracted beams which still remain in the MPE region 1750 aftereach interaction can experience additional interactions. Each of theseadditional interactions results in some of the power of the beamszero-order diffracting and continuing on in the same direction, whilesome of the power of the beams is diffracted in new directions. Thisresults in spatially distributed sets of diffracted beams that havepropagation angles centered around each of the propagation directionsindicated by the center points of the FOV rectangles in the k-spaceannulus shown in FIG. 17C. This is represented by the double-sidedarrows between each pair of FOV rectangles in the k-space annulus. Inother words, beams of light propagating in the MPE region 1750 cantransition from any propagation state represented by one of the FOVrectangles in the k-space annulus to any other of these propagationstates.

As any given input beam of light propagates within the MPE region 1750,it is split into many diffracted beams which can only travel in fourallowed directions—each direction being defined by the correspondingk-vector, or point, within the FOV rectangles in the annulus of thek-space diagram in FIG. 17C. (This is true for any input beam of lightpropagating within the MPE region 1750. However, the four alloweddirections will be slightly different depending on the propagation angleat which each initial input beam enters the MPE region 1750.) And sinceportions of the power of any given input beam of light are diffractedinto the same four propagation directions after any number ofinteractions with the MPE region 1750, image information is preservedthroughout these interactions. The additional propagation directionwhich is permitted in the MPE region 1750, as compared to the MPE region1650 described with respect to FIGS. 16A-16M, can result in even furtherimprovements in the evenness of illumination in the EPE region 1760.This can be seen in the diagrams shown in FIGS. 17D-17G.

FIG. 17D is a diagram of the first generation of interactions between aninput beam and the MPE region 1750 of the eyepiece waveguide 1700. FIG.17D shows an input beam that enters the MPE region 1750 from the ICGregion 1740. The input beam is shown propagating in the direction whichcorresponds to the center point, or k-vector, of the FOV rectanglelocated near the 9 o'clock position of the k-space annulus in FIG. 17C.

The MPE region 1750 can include many sub-1 μm features. And at everyinteraction with the MPE region, a ˜1 mm-diameter beam will split into 4beams (with the same diameter but a fraction of the original power ofthe input beam) propagating in 4 different directions in TIR. Onedirection corresponds to zero-order diffraction and is the originalangle in the plane of the waveguide. The other three directions dependon the grating vectors G and H of the MPE region 1750. As shown, thefirst generation of interactions between the input beam and the MPEregion 1750 results in four beams: some portion of the power of theinput beam simply reflects, as output₁, from the top or bottom surfaceof the eyepiece waveguide 1700 and continues on in the same x-ydirection as the input beam (i.e., the 0^(th) order diffraction); someportion of the power of the input beam interacts with the grating and isdiffracted downward as output₂; some portion of the power of the inputbeam interacts with the grating and is diffracted upward as output₃; andsome portion of the power of the input beam interacts with the gratingand is diffracted to the right as output₄. The output₂ beam is shownpropagating in the direction which corresponds to the center point, ork-vector, of the FOV rectangle located near the 6 o'clock position ofthe k-space annulus in FIG. 17C, while the output₃ beam is shownpropagating in the direction which corresponds to the center point, ork-vector, of the FOV rectangle located near the 12 o'clock position, andthe output₄ beam is shown propagating in the direction which correspondsto the center point, or k-vector, of the FOV rectangle located near the3 o'clock position. After this first generation of interactions, theoutput₁ beam, the output₂ beam, the output₃ beam, and the output₄ beamhave different propagation angles, but they are all still propagatingwithin the MPE region 1750 and may therefore have additionalinteractions with the MPE region, as shown in FIGS. 17E-17G. Althoughnot illustrated, other input beams that enter the MPE region 1750 withdifferent propagation angles will behave similarly but with slightlydifferent input and output angles.

FIG. 17E is a diagram of the second generation of interactions betweenan input beam and the MPE region 1750 of the eyepiece waveguide 1700.The beams related to the first generation of interactions are shown withdashed lines, while the beams related to the second generation ofinteractions are shown with solid lines. As shown in FIG. 17D, each ofthe output beams, output₁, output₂, output₃, and output₄, from the firstgeneration of interactions can now undergo similar interactions with theMPE region 1750 as occurred in the previous generation. Namely, someportion of the power of the output₁ beam from FIG. 17D simply continueson in the same x-y direction, while other portions of the power of thatbeam interact with the grating and are diffracted in the directionscorresponding to the FOV rectangles located near the 12 o'clockposition, near the 3 o'clock position, and near the 6 o'clock position.Similarly, some portion of the power of the output₂ beam from FIG. 17Dsimply continues toward the EPE region 1760, while other portions of thepower of that beam interact with the grating and are diffracted in thedirections indicated by the FOV rectangles located near the 9 o'clockposition, near the 12 o'clock position, and near the 3 o'clock position.Further, some portion of the power of the output₃ beam from FIG. 17Dsimply continues in the direction indicated by the FOV rectangle locatednear the 12 o'clock position, while other portions of the power of thatbeam interact with the grating and are diffracted in the directionsindicated by the FOV rectangles located near the 3 o'clock position,near the 6 o'clock position, and near the 9 o'clock position. Finally,some portion of the power of the output₄ beam from FIG. 17D simplycontinues in the direction indicated by the FOV rectangle located nearthe 3 o'clock position, while other portions of the power of that beaminteract with the grating and are diffracted in the directions indicatedby the FOV rectangles located near the 6 o'clock position, near the 9o'clock position, and near the 12 o'clock position.

FIG. 17F is a diagram of the third generation of interactions between aninput beam and the MPE region 1750 of the eyepiece waveguide embodiment1700. The beams related to the first and second generations ofinteractions are shown with dashed lines, while the beams related to thethird generation of interactions are shown with solid lines. As shown inFIG. 17F, each of the output beams which resulted from the secondgeneration of interactions can once more experience similar interactionswith the MPE region 1750 as occurred in the previous generations.

FIG. 17G is a diagram of the fourth generation of interactions betweenan input beam and the MPE region 1750 of the eyepiece waveguideembodiment 1700. The beams related to the first, second, and thirdgenerations of interactions are shown with dashed lines, while the beamsrelated to the fourth generation of interactions are shown with solidlines. After all these interactions, all of the resulting beams arepropagating in one of the four permitted propagation directions with theMPE region 1750 for any given input beam: the direction corresponding tothe FOV rectangle located near the 9 o'clock position; the directioncorresponding to the FOV rectangle located near the 12 o'clock position;the direction corresponding to the FOV rectangle located near the 3o'clock position; or the direction corresponding to the FOV rectanglelocated near the 6 o'clock position of the k-space annulus. Althoughthere are nodes where some of these beams may intersect with one anotherwhile propagating through the MPE region 1750, the locations of thosenodes have an even more complex distribution than in the case of the MPEregion 1650 which was illustrated in FIGS. 16A-16M. Further, these nodesare even less likely to result in interference between two in-phasebeams. Accordingly, this MPE region 1750 may result in an even moreuniform illumination of the EPE region 1760.

By way of summary, the MPE regions described herein are capable of someor all of the following advantages: MPE regions can expand an imagepupil in multiple directions at once; MPE regions can create dense,non-periodic arrays of output pupils; MPE regions can reduceinterference effects between light paths through the waveguide;MPE-based eyepiece waveguides can achieve improved luminance uniformitywith reduced high-frequency striations and with high image sharpness.

Example AR Eyepiece Waveguides with Multiple Distinct Regions forReplicating Input Beams

FIG. 18A illustrates an example eyepiece waveguide 1800 with an ICGregion 1840, two orthogonal pupil expander (OPE) regions 1850 a, 1850 b,and an exit pupil expander (EPE) region 1860. FIG. 18A also includesk-space diagrams which illustrate the effect of each of these componentsof the eyepiece waveguide 1800 in k-space. The ICG region 1840, OPEregions 1850 a, 1850 b, and EPE region 1860 of the eyepiece waveguide1800 include various diffractive features which couple input beams intothe eyepiece waveguide 1800 to propagate via guided modes, replicate thebeams in a spatially distributed manner, and cause the replicated beamsto exit the eyepiece waveguide and be projected toward the user's eye.In particular, the eyepiece waveguide 1800 includes multiple distinctand/or non-contiguous regions for replicating input beams. Replicatedbeams from these distinct regions can be re-combined in a common exitpupil region.

The eyepiece waveguide 1800 illustrated in FIG. 18A is similar to theeyepiece waveguide 1400 illustrated in FIG. 14A except that it includestwo OPE regions 1850 a, 1850 b instead of one. Recall that the ICGregion 1440 in the eyepiece waveguide 1400 diffracted input beams intothe +1 and −1 diffractive orders but that the beams in one of thesediffractive orders propagated away from the OPE region 1450 and wereultimately lost from the eyepiece waveguide. Accordingly, a portion ofthe light from the input beams was lost. The eyepiece waveguide 1800shown in FIG. 18A remedies this by including two OPE regions 1850 a,1850 b, one on either side of the ICG region 1840. In this way, theeyepiece waveguide 1800 can make use of both the +1 and the −1diffractive orders of the ICG 1840.

The operation of the ICG region 1840 is similar to what has beendescribed with respect to the ICG region 1440 in FIGS. 14A and 14B. Thesame k-space diagram, KSD1, shown in FIG. 14B is also illustrative ofthe FOV rectangle corresponding to the set of input beams that areincident on the ICG region 1840 in FIG. 18A. Namely, before the inputbeams are incident on the ICG region 1840, the FOV rectangle is centeredat the origin of the k-space diagram.

K-space diagram KSD2 in FIG. 18A illustrates the operation, in k-space,of the ICG region 1840. Namely, as discussed with respect to thecorresponding k-space diagram in FIG. 14B, the ICG region 1840 isassociated with two grating vectors which respectively translate the FOVrectangle to the 3 o'clock and 9 o'clock positions inside the k-spaceannulus. The translated FOV rectangle located at the 3 o'clock positionrepresents diffracted beams which propagate toward the right OPE region1850 b, while the translated FOV rectangle located at the 9 o'clockposition represents diffracted beams which propagate toward the left OPEregion 1850 a.

The operation of the left OPE region 1850 a is also similar to what hasbeen described with respect to the OPE region 1450 in FIGS. 14A and 14B.K-space diagram KSD3 a illustrates the k-space operation of the left OPEregion 1850 a and shows that its diffraction grating translates the FOVrectangle from the 9 o'clock position in the k-space annulus to the 6o'clock position. The FOV rectangle located at the 6 o'clock positionrepresents diffracted beams which propagate in the −y-direction towardthe EPE region 1860.

The operation of the right OPE region 1850 b is similar to that of theleft OPE region 1850 a except that its associated grating vectors aremirrored about a vertical line with respect to those of the left OPEregion 1850 a. This is due to the fact that the lines of the diffractiongrating in the right OPE region 1850 b are mirrored about a verticalline with respect to those of the diffraction grating in the left OPEregion 1850 a. As a result of this orientation of the lines of thediffraction grating in the right OPE region 1850 b, the effect of thisgrating in k-space is to translate the FOV rectangle from the 3 o'clockposition in the k-space annulus to the 6 o'clock position, as shown ink-space diagram KSD3 b. The translated FOV rectangles in KSD3 a and KSD3b are in the same location at the 6 o'clock position of the k-spaceannulus. Thus, although the power of each input beam is split into +1and −1 diffractive orders by the ICG region 1840, and those distinctdiffractive orders travel different paths through the eyepiece waveguide1800, they nevertheless arrive at the EPE region 1860 with the samepropagation angle. This means that the separate diffractive orders ofeach input beam which follow different propagation paths through theeyepiece waveguide 1800 ultimately exit the EPE region 1860 with thesame angle and therefore represent the same point in the projectedimage.

Finally, the operation of the EPE region 1860 is also similar to whathas been described with respect to the EPE region 1460 in FIGS. 14A and14B. K-space diagram KSD4 illustrates the k-space operation of the EPEregion 1860 and shows that its diffraction grating translates the FOVrectangle located at the 6 o'clock position (which consists of lightbeams from both OPE regions 1850 a, 1850 b) of the k-space annulus backto the center of the k-space diagram. As already discussed elsewhere,this represents that the EPE region 1860 out-couples the beams of lightgenerally in the z-direction toward the user's eye.

FIGS. 18B and 18C illustrate top views of the EPE region 1860 of theeyepiece waveguide 1800 shown in FIG. 18A. The EPE region 1860 issupported directly in front of the user's eye 210. As discussedelsewhere herein (see FIGS. 12A and 12B), the EPE region 1860 projectssets of replicated output beams, with each set of replicated outputbeams having a propagation angle which corresponds to one of the inputbeams which are projected into the eyepiece waveguide.

FIG. 18B illustrates one of these sets of replicated output beams. Inthis particular case, the replicated output beams 1861 exit the EPEregion 1860 traveling from left to right. In other words, the replicatedoutput beams 1861 have a propagation direction with a component in the+x-direction. This propagation angle of the replicated output beams 1861results in some of them having a greater tendency to intersect with theuser's eye 210 than others. In particular, the replicated output beams1861 which exit from the left-hand portion of the EPE region 1860 have agreater tendency to intersect with the user's eye 210 due to the centralposition of the eye 210 and the left-to-right propagation of the lightbeams. These light beams are illustrated with solid lines. Meanwhile,the replicated output beams 1861 which exit from the right-hand portionof the EPE region 1860 have a greater tendency to miss the eye 210.These light beams are illustrated with dashed lines.

FIG. 18B also includes a k-space diagram, KSD5, which illustrates thestate of the output beams, in k-space, after the EPE region hastranslated the FOV rectangle back to the origin of the diagram. The FOVrectangle is illustrated with two halves. Each of the halves representshalf of the horizontal field of view of the eyepiece waveguide 1800. Theshaded right half 1832 of the FOV rectangle includes the k-vectors withcomponents in the +k_(x)-direction. These are the k-vectorscorresponding to the output beams 1861 which exit the EPE region 1860with the type of left-to-right propagation illustrated in FIG. 18B.Although only one set of replicated output beams 1861 is illustratedexiting the EPE region 1860, all of the output beams whose k-vectors liein the shaded right half 1832 of the FOV rectangle would similarly exitthe EPE region with propagation directions going left-to-right. Thus, itis true for all of the output beams whose k-vectors lie in the shadedright half 1832 of the FOV rectangle that those beams exiting theleft-hand side of the EPE region 1860 will have a greater tendency tointersect with the eye 210 than those output beams which exit theright-hand side of the EPE region.

FIG. 18C illustrates another set of replicated light beams 1862 whichexit the EPE region 1860 of the eyepiece waveguide 1800. But in thiscase, the replicated output beams 1862 exit the EPE region 1860traveling from right to left. In other words, the replicated outputbeams 1862 have a propagation direction with a component in the−x-direction. This propagation angle of the replicated output beams 1862leads to the opposite observation of that which was drawn from FIG. 18B.Namely, for the right-to-left propagating output beams 1862, the beamsexiting from the right-hand portion of the EPE region 1860 (illustratedwith solid lines) have a greater tendency to intersect with the eye 210,while those light beams which exit from the left-hand portion of the EPEregion (illustrated with dashed lines) have a greater tendency to missthe eye.

With reference to the k-space diagram, KSD5, included with FIG. 18C, theoutput beams whose k-vectors lie in the shaded left half 1831 of the FOVrectangle are those which exit the EPE region 1860 with the type ofright-to-left propagation shown in FIG. 18C. Although all of the outputbeams whose k-vectors lie in the shaded left half 1831 of the FOVrectangle will have differing propagation angles, they all share theproperty that the beams exiting the right-hand side of the EPE region1860 will have a greater tendency to intersect with the eye 210 than theoutput beams which exit from the left-hand side of the EPE region.

The conclusion which can be drawn from FIGS. 18B and 18C is that, basedon the light beams which actually enter the user's eye 210, half of theEPE region 1860 contributes predominantly to one half of the horizontalfield of view, while the other half of the EPE region contributespredominantly to the other half of the horizontal field of view. Basedon this observation, the field of view which can be projected by aneyepiece waveguide can be expanded in at least one dimension beyond therange of propagation angles supported by the eyepiece in guided modesbecause it is unnecessary to project the entire FOV rectangle from everyportion of the EPE region 1960. This is illustrated in FIG. 19.

Example AR Eyepiece Waveguides with Expanded Field of View

FIG. 19 illustrates an embodiment of an eyepiece waveguide 1900 with anexpanded field of view. The eyepiece waveguide 1900 includes an ICGregion 1940, a left OPE region 1950 a, a right OPE region 1950 b, and anEPE region 1960. At a macroscopic level, the eyepiece waveguide 1900shown in FIG. 19 can be identical to the eyepiece waveguide 1800 shownin FIG. 18A. However, some of the diffractive features in the eyepiecewaveguide 1900 can be designed with characteristics which allow forincreased field of view in at least one dimension. These features can beclearly understood based on the k-space operation of the eyepiecewaveguide 1900, which is illustrated by the k-space diagrams shown inFIG. 19.

The k-space diagrams shown in FIG. 19 have larger FOV rectangles thanthose which are shown in FIG. 18A. This is because the FOV rectangles inthe k-space diagrams in FIG. 18A were constrained to not have anydimension larger than the width of the k-space annulus. This constraintensured that those FOV rectangles could fit entirely in the k-spaceannulus, at any position around the annulus, and therefore that all ofthe beams represented by the k-vectors in the FOV rectangles couldundergo guided propagation within the eyepiece waveguide 1800 whilepropagating in any direction in the plane of the eyepiece. In theexample embodiment of FIG. 19, however, the FOV rectangles have at leastone dimension (e.g., the k_(x) dimension) which is larger than the widthof the k-space annulus. In some embodiments, one or more dimensions ofthe FOV rectangles can be up to 20%, up to 40%, up to 60%, up to 80%, orup to 100% larger than the width of the k-space annulus.

For the particular embodiment illustrated in the k-space diagrams ofFIG. 19, the horizontal dimension of the FOV rectangles is wider thanthe k-space annulus. The horizontal dimension of the FOV rectanglescorresponds to the horizontal spread in the propagation angles of theinput beams which are projected into an eyepiece waveguide. Thus, sincethe eyepiece waveguide 1900 is illustrated as being capable of use withFOV rectangles having larger horizontal dimensions, this means that thehorizontal field of view of the eyepiece waveguide is increased. For thecase of an eyepiece waveguide (surrounded by air) with refractive index1.8, whereas the eyepiece waveguide 1800 shown in FIG. 18A is generallycapable of achieving FOVs of 45° by 45°, the eyepiece waveguide 1900shown in FIG. 19 is capable of achieving FOVs of up to 90° by 45°,though some embodiments of the eyepiece waveguide may be designed forsmaller FOVs of −60° by 45° so as to satisfy typical design constraintsof eyebox volume—it may be advantageous to send some portion of the FOVto both sides of the eyepiece waveguide to provide an adequately-sizedeyebox—and to avoid screen door artifacts resulting from sparsely spacedoutput beams. Although the techniques for expanding the field of view ofthe eyepiece waveguide 1900 are described in the context of expandedhorizontal fields of view, the same techniques can also be used toexpand the vertical field of view of the eyepiece waveguide 1900.Moreover, in later embodiments, similar techniques are shown forexpanding both the horizontal and vertical fields of view of an eyepiecewaveguide.

It can be seen by inspection of the k-space diagrams in FIG. 19 thatalthough the illustrated FOV rectangles may not fit entirely within thek-space annulus when located at certain positions around the annulus,they can still fit entirely within the annulus when located at otherpositions. For example, if one dimension of the FOV rectangle is largerthan the width of the k-space annulus, then the FOV rectangle may notfit entirely within the annulus when the FOV rectangle is located at ornear the axis of the enlarged dimension: an FOV rectangle which islarger in the k_(x) dimension than the width of the k-space annulus maynot fit entirely within the annulus when the FOV rectangle is located ator near the k_(x)-axis (i.e., at or near the 3 o'clock and 9 o'clockpositions); similarly, an FOV rectangle which is larger in the k_(y)dimension than the width of the k-space annulus may not fit entirelywithin the annulus when the FOV rectangle is located at or near thek_(y)-axis (i.e., at or near the 12 o'clock and 6 o'clock positions).However, such an FOV rectangle may still fit entirely within the k-spaceannulus when it is located at or near the opposite axis: an FOVrectangle which is larger in the k_(x) dimension than the width of thek-space annulus may still fit entirely within the annulus when the FOVrectangle is located at or near the k_(y)-axis (i.e., at or near the 12o'clock and 6 o'clock positions); similarly, an FOV rectangle which islarger in the k_(y) dimension than the width of the k-space annulus maystill fit entirely within the annulus when the FOV rectangle is locatedat or near the k_(x)-axis (i.e., at or near the 3 o'clock and 9 o'clockpositions). This is because there is more area in the k-space annulus inthe azimuthal direction to accommodate larger FOV rectangles than in theradial direction.

The radial size of the k-space annulus corresponds to the range ofpropagation angles in the direction normal to the plane of the waveguide(i.e., the thickness direction) which support guided propagation modes.This range of propagation angles is constrained by Snell's Law and therequirements which must be satisfied for TIR to occur. In contrast, aspread of k-vectors in the azimuthal dimension of the k-space annuluscorresponds to a spread of propagation angles in the in-plane directionof the planar waveguide. Since the spread of propagation angles withinthe plane of the planar waveguide is not limited by the same constraintsas in the thickness direction, a wider range of beam propagation anglescan be supported.

Moreover, it is possible to convert a spread of propagation angles inthe thickness direction of an eyepiece waveguide to a spread ofpropagation angles in the in-plane direction, and vice versa. When adiffraction grating (or other group of diffractive features) translatesan FOV rectangle from one position in the k-space annulus to anothersuch that the set of beams represented by the FOV rectangle are thenpropagating in a new direction, this also causes some of the beams whichwere previously spread out in the thickness direction of the planarwaveguide to instead be spread out in the in-plane direction, and viceversa. This can be seen when, for example, a diffraction gratingtranslates an FOV rectangle from the 9 o'clock position in the k-spaceannulus to the 6 o'clock position. While in the 9 o'clock position, thespread of beams in the k_(x) direction corresponds to a physical spreadin the thickness direction of the waveguide since at that location thek_(x) direction corresponds to the radial direction of the k-spaceannulus. However, at the 6 o'clock position, the spread of beams in thek_(x) direction corresponds to a physical spread in the in-planedirection of the waveguide since at that location the k_(x) directioncorresponds to the azimuthal direction of the k-space annulus.

Using these observations, the FOV of an eyepiece waveguide can beincreased by: dividing an FOV rectangle into multiple sub-portions;using diffractive features to replicate the beams, in a spatiallydistributed manner, belonging to the multiple sub-portions of the FOV;and using diffractive features to re-assemble the multiple sub-portionsof the FOV at the exit pupil of the eyepiece waveguide such that thebeams corresponding to each sub-portion of the FOV have the correctpropagation angles to re-create the original image. For example,diffractive features can be used to translate each sub-portion of theFOV rectangle to one or more locations in k-space such that theyultimately have the same relative position with respect to the othersub-portions of the FOV rectangle as in the original image.

In some embodiments, the multiple sub-portions of the FOV can partiallyoverlap one another (e.g., different pairs of FOV sub-portions caninclude some of the same input beams), as this can help ease theconstraints for re-assembling the entire FOV at the exit pupil of thewaveguide and can help to ensure that all of the beams are present. Forexample, in some embodiments, a pair of sub-portions of the input imageFOV may overlap by no more than 10%, no more than 20%, no more than 30%,no more than 40%, no more than 50%, or more.

K-space diagram KSD2 in FIG. 19 illustrates the k-space operation of theICG region 1940 on the input beams which are projected into the eyepiecewaveguide 1900. As discussed elsewhere herein, the input beams which areprojected into the eyepiece waveguide 1900 can be represented by an FOVrectangle which is centered at the origin of the k-space diagram KSD2.The ICG region 1940 translates the location of this FOV rectangle ink-space based on its associated grating vectors. In the case of the ICGregion 1840 illustrated in FIG. 18A, the ICG region was designed suchthat its associated grating vectors G₁, G⁻¹ had magnitudes equal to thedistance from the origin of the k-space diagram to the midpoint of thek-space annulus. This caused the FOV rectangle to be centered within thek-space annulus. But the ICG region 1940 illustrated in FIG. 19 can bedesigned to have larger grating vectors. And, as already discussed, theset of input beams which are projected into the eyepiece waveguide 1900can have at least one dimension in k-space that is larger than the widthof the k-space annulus.

In some embodiments, ICG region 1940 can be designed such that itsgrating vectors G₁, G⁻¹ translate the enlarged FOV rectangle far enoughfrom the origin of the k-space diagram such that no portion of theenlarged FOV rectangle lies inside the inner disk of the k-spacediagram. To achieve this goal in the case of an FOV rectangle whosehorizontal dimension is twice as large as the width of the k-spaceannulus, the magnitude of the grating vectors G₁, G⁻¹ of the ICG 1940would need to be approximately equal to the radius of the outer disk ofthe k-space diagram. Meanwhile, to achieve this goal in the case of anFOV rectangle whose horizontal dimension is just slightly larger thanthe width of the k-space annulus, the magnitude of the grating vectorsG₁, G⁻¹ of the ICG region 1940 would need to be greater than thedistance from the origin of the k-space diagram to the midpoint of thek-space annulus. Mathematically, this means

$\frac{n_{2}\omega}{c} \geq {{G_{1},G_{- 1}}} > {\frac{1}{2}\left( {\frac{n_{2}\omega}{c} + \frac{n_{1}\omega}{c}} \right)}$

which gives

$\frac{n_{2}\omega}{c} \geq {\frac{n_{2}}{\Lambda}} > {\frac{1}{2}{\left( {\frac{n_{2}\omega}{c} + \frac{n_{1}\omega}{c}} \right).}}$

(Note: This equation can also be applied to the other eyepiece waveguideembodiments described herein, such as, for example, those shown in FIGS.20-22 and described below.)

In other words, this technique for expanding the field of view of theeyepiece waveguide 1900 means that the grating vectors G₁, G⁻¹ of theICG region 1940 are designed to be longer than in embodiments where thefield of view is constrained in all dimensions by the range ofpropagation angles which can fit within the radial dimension of thek-space annulus of a given eyepiece waveguide. Since the length of thegrating vectors G₁, G⁻¹ is increased by decreasing the grating period,Λ, this means that the ICG region 1940 has a finer pitch than what wouldconventionally be used for light of a given angular frequency, ω, toensure that all of the input beams can be diffracted into guided modes.

Of course, according to the embodiment illustrated in FIG. 19, thelarger size of the FOV rectangle and the longer grating vectors G₁, G⁻¹cause portions of the translated FOV rectangles, after diffraction bythe ICG region 1940, to extend beyond the outer perimeter of the largerdisk in the k-space diagram. Since k-vectors outside this disk are notpermitted, the input beams corresponding to those k-vectors are notdiffracted by the ICG region 1940. Instead, only the input beamscorresponding to k-vectors in the shaded portions of the translated FOVrectangles in KSD2 enter guided propagation modes within the eyepiecewaveguide 1900. The input beams which would diffract into the +1 orderwith k-vectors that would lie outside the outer disk of the k-spacediagram are not permitted to diffract and are therefore lost. Similarly,the input beams which would diffract into the −1 order with k-vectorsthat would lie outside the outer disk of the k-space diagram are notpermitted to diffract and are therefore lost. Fortunately, the beamswhich are lost from each of these diffractive orders are not the sameones. This allows the full field of view to be recovered at the EPEregion 1960. Even though neither the truncated FOV rectangle located atthe 3 o'clock position of the k-space diagram KSD2, nor the truncatedFOV rectangle located at the 9 o'clock position, includes the completeset of input beams, when these truncated FOV rectangles areappropriately recombined at the EPE region 1960, the complete set ofinput beams can be recovered.

The k-space diagrams KSD3 a and KSD3 b respectively illustrate thek-space operation of the diffraction gratings in the left OPE region1950 a and the right OPE region 1950 b. As discussed with respect toFIG. 18A, these OPE regions can include diffraction gratings which areoriented so as to translate the FOV rectangles located at the 3 o'clockand 9 o'clock positions to the 6 o'clock position. In the embodimentillustrated in FIG. 19, however, the orientations of the diffractiongratings in the OPE regions 1950 a, 1950 b may need to be adjusted inorder to accomplish this aim. Specifically, since the grating vectorsG₁, G⁻¹ associated with the ICG region 1940 may no longer terminate atthe midpoint of the k-space annulus in the 3 o'clock and 9 o'clockpositions, the magnitudes and directions of the grating vectorsassociated with the OPE regions may need to be adjusted in order totranslate the FOV rectangles to a location at the 6 o'clock position(e.g., one which is centered in the k-space annulus in thek_(y)-direction). These adjustments can be accomplished by altering theorientations of the grating lines in the OPE regions 1950 a, 1950 band/or by changing their grating periods, A, in comparison to the OPEregions in an embodiment without an expanded FOV.

The shaded right-hand portion of the FOV rectangles in KSD3 a representsa first sub-portion of the FOV, while the shaded left-hand portion ofthe FOV rectangles in KSD3 b represents a second sub-portion of the FOV.In the illustrated embodiment, these FOV sub-portions overlap in thecentral region of the FOV rectangles.

K-space diagram KSD3 a illustrates that when the FOV rectangle locatedat the 9 o'clock position is translated to the 6 o'clock position, onlythe beams corresponding to the shaded right-hand region of the FOVrectangle are present. K-space diagram KSD3 b shows the same phenomenonexcept that the absent beams are the ones whose k-vectors are located onthe opposite side of the FOV rectangle. Finally, k-space diagram KSD4shows that when the two truncated FOV rectangles are superimposed at the6 o'clock position of the k-space annulus, the unshaded portions of theFOV rectangle are filled in, meaning that all of the beams which make upthe complete FOV of the input image are now present and can be projectedout of the eyepiece waveguide 1900 toward the user's eye by thediffraction grating in the EPE region 1960. Similar to the embodiment inFIG. 18A, the EPE region 1960 translates the FOV rectangle back to theorigin in k-space diagram KSD4. Importantly, the two truncated FOVrectangles from the 9 o'clock and 3 o'clock positions should betranslated to the 6 o'clock position in such a manner as to maintain therelative positions of the shaded regions within the original FOVrectangle. This ensures that the beams of light in each sub-portion ofthe FOV have the correct propagation angles so as to re-create theoriginal image.

What this means in physical terms is that the eyepiece waveguide 1900divides the image field of view into multiple parts. The light beamscorresponding to each of these parts of the image field of viewpropagate through the eyepiece waveguide 1900 along different paths,where they may be replicated in a spatially distributed manner bydifferent OPE regions 1950 a, 1950 b. And ultimately the separate partsof the image field of view are recombined in the EPE region 1960 to beprojected toward the user's eye.

In some embodiments, the various diffraction gratings of the eyepiece1900 can be designed such that there is overlap between the subsets ofbeams which are supplied to the EPE region 1960 by the respective OPEregions 1950 a, 1950 b. In other embodiments, however, the diffractiongratings can be designed such that each OPE region 1950 a, 1950 bsupplies a unique subset of the beams which are required to fullyre-create the input image.

Example AR Eyepiece Waveguides with Expanded Field of View andOverlapping MPE and EPE Regions

While FIG. 19 illustrates an embodiment of an eyepiece waveguide with anexpanded FOV which uses OPE regions to replicate the input beams, otherembodiments can advantageously use MPE regions. FIGS. 20A-20L illustrateone such example embodiment.

FIG. 20A illustrates an embodiment of an expanded FOV eyepiece waveguide2000 with an MPE region 2050 which is overlapped by an EPE region 2060.The eyepiece waveguide 2000 can achieve an expanded field of view whichcan be larger than the range of propagation angles that can be supportedin guided propagation modes in the thickness direction of the waveguide.The eyepiece waveguide 2000 has a first surface 2000 a and a secondsurface 2000 b. As discussed further below, different diffractivefeatures can be formed on or in the opposite surfaces 2000 a, 2000 b ofthe eyepiece waveguide 2000. The two surfaces 2000 a, 2000 b of theeyepiece waveguide 2000 are illustrated in FIG. 20A as being displacedin the x-y plane with respect to one another. However, this is only forpurposes of illustration to be able to show the different diffractivefeatures formed on or in each surface; it should be understood that thefirst surface 2000 a and the second surface 2000 b are aligned with oneanother in the x-y plane. In addition, while the MPE region 2050 and theEPE region 2060 are illustrated as being the same size and exactlyaligned in the x-y plane, in other embodiments they may have somewhatdifferent sizes and may be partially misaligned. In some embodiments,the MPE region 2050 and the EPE region 2060 overlap one another by atleast 70%, at least 80%, at least 90%, or at least 95%.

The eyepiece waveguide 2000 includes an ICG region 2040, an MPE region2050, and an EPE region 2060. The ICG region 2040 receives a set ofinput beams from a projector device. As described elsewhere herein, theinput beams can propagate from the projector device through free spacegenerally in the z-direction until they are incident upon the ICG region2040. The ICG region 2040 diffracts those input beams so that they all,or at least some, enter guided propagation modes within the eyepiecewaveguide 2000. The grating lines of the ICG region 2040 can be orientedso as to direct the diffracted beams in the −y-direction toward the MPEregion 2050.

The MPE region 2050 can include a plurality of diffractive featureswhich exhibit periodicity along multiple axes. The MPE region 2050 maybe composed of an array of scattering features arranged in a 2D lattice.The individual scattering features can be, for example, indentations orprotrusions of any shape. The 2D array of scattering features hasassociated grating vectors, which are derived from the reciprocallattice of that 2D lattice. As one example, the MPE region 2050 could bea 2D diffraction grating composed of a crossed grating with gratinglines that repeat along two or more directions of periodicity. Thediffractive features which make up the MPE region 2050 can have arelatively low diffractive efficiency (e.g., 10% or less). As discussedherein, this allows beams of light to be replicated in a spatiallydistributed manner in multiple directions as they propagate through theMPE region 2050.

FIG. 20B illustrates a portion of an example 2D grating, along with itsassociated grating vectors, which can be used in the MPE region 2050 ofthe eyepiece waveguide 2000. A crossed grating is illustrated, thoughthe 2D periodic grating could instead be made up of individualscattering features located at, for example, the intersection points ofthe illustrated grating lines. The 2D grating has a first set of gratinglines 2056 which repeat along a first direction of periodicity. Thesegrating lines 2056 have an associated fundamental grating vector G whichpoints along the direction of periodicity of the first set of gratinglines 2056 and has a magnitude equal to 2π/a, where a is the period ofthe first set of grating lines 2056. The 2D grating shown in FIG. 20B isalso associated with harmonics of the first fundamental grating vectorG. These include −G and higher-order harmonics, such as 2G, −2G, etc.The 2D grating in the MPE region 2050 also has a second set of gratinglines 2057 which repeat along a second direction of periodicity. In someembodiments, the first and second directions of periodicity are notperpendicular. The second set of grating lines 2057 have an associatedfundamental grating vector H which points along the direction ofperiodicity of the second set of grating lines, with a magnitude equalto 2π/b, where b is the period of the second set of grating lines 2057.The 2D grating shown in FIG. 20B is also associated with harmonics ofthe second fundamental grating vector H. These include −H andhigher-order harmonics, such as 2H, −2H, etc. Finally, any 2D array ofdiffractive features will also have associated grating vectors whichpoint in directions determined by integer linear combinations(superpositions) of the basis grating vectors, G and H. In theillustrated embodiment, these superpositions result in additionalgrating vectors which are also shown in FIG. 20B. These include, forexample, −G, −H, H+G, H−G, G−H, and −(H+G). Although FIG. 20B onlyillustrates the first order grating vectors, and their superpositions,associated with the 2D diffraction grating, higher-order grating vectorsmay also exist.

FIG. 20C is a k-space diagram, KSD1, which illustrates the k-spaceoperation of the ICG region 2040 of the eyepiece waveguide 2000. The FOVrectangle centered at the origin of KSD1 represents the set of inputbeams which are projected toward the ICG region 2040 by a projectordevice. The dimension of the FOV rectangle in the k_(x)-directionrepresents the FOV of the input beams in the x-direction, while thedimension of the FOV rectangle in the k_(y)-direction represents the FOVof the input beams in the y-direction. As illustrated, in thisparticular embodiment, the k_(x) dimension of the FOV rectangle islarger than the width of the k-space annulus.

Since the MPE region 2050 is located in the −y-direction from the ICGregion 2040 according to the physical layout of the eyepiece waveguide2000 shown in FIG. 20A, the diffraction grating in the ICG region 2040can be designed so as to diffract input beams in that direction. Thus,KSD1 in FIG. 20C shows that the ICG region 2040 translates the FOVrectangle from the origin of the k-space diagram to a location on the−k_(y)-axis at the 6 o'clock position in the k-space annulus. At thisparticular position, the wider dimension of the FOV rectangle isoriented in the azimuthal direction of the k-space annulus and so theFOV rectangle fits entirely within the annulus. This means that all ofthe beams represented by the FOV rectangle enter guided propagationmodes within the eyepiece waveguide 2000 and propagate generally in the−y-direction toward the MPE region 2050.

Just as in other MPE regions discussed herein (e.g., 1650, 1750), theMPE region 2050 expands the image pupil in multiple directions byreplicating the input beams in a spatially distributed manner as theypropagate through it. FIGS. 20D-20F and 20H illustrate this behavior ofthe MPE region 2050 in k-space.

FIG. 20D is a k-space diagram, KSD2, which illustrates part of thek-space operation of the MPE region 2050 of the eyepiece waveguide 2000.The k-space diagram includes a shaded FOV rectangle located at the 6o'clock position of the k-space annulus. This is the location of the FOVrectangle after the ICG region 2040 has coupled the input beams into theeyepiece waveguide 2000 and diffracted them toward the MPE region 2050.FIG. 20D shows how the 2D grating in the MPE region 2050 translates theFOV rectangle using the grating vectors shown in FIG. 20B. Since thereare eight grating vectors, the MPE region 2050 attempts to translate theFOV rectangle from the 6 o'clock position in the k-space annulus toeight possible new locations in the k-space diagram. Of these eightpossible locations, five fall completely outside the outer periphery ofthe k-space diagram. These locations are illustrated with unshaded FOVrectangles. Since k-vectors outside the outer periphery of the k-spacediagram are not permitted, none of those five grating vectors results indiffraction. There are, however, three grating vectors (i.e., G, −H, andG−H) which do result in translations of the FOV rectangle to newpositions at least partially within the bounds of the k-space diagram.One of these locations is at the 9 o'clock position in the k-spaceannulus, another is at the 12 o'clock position, and the last is at the 3o'clock position. Since k-vectors at these locations are permitted anddo result in guided propagation modes, the FOV rectangles at theselocations are shaded to indicate that beams of light are diffracted intothose three states.

In the case of the 9 o'clock and 3 o'clock positions in the k-spaceannulus, the translated FOV rectangles do not fit completely within theannulus because their k_(x) dimension is larger than the width of theannulus. Thus, the translated FOV rectangles at these locations aretruncated, meaning that the beams whose k-vectors fall outside the outerperiphery of the k-space diagram are not guided. This is represented inKSD2 by the unshaded portions of the translated FOV rectangles at the 9o'clock in 3 o'clock positions. This means that the set of beams whichare spreading through the MPE region 2050 in the +x and the −xdirections, respectively, do not each include all of the original set ofinput beams. The set of beams propagating through the MPE region 2050 inthe +x direction are missing the beams corresponding to the right-handside of the FOV rectangle, while the set of beams propagating in the −xdirection are missing the beams corresponding to the left-hand side ofthe FOV rectangle. Collectively, however, all of the beams which make upthe FOV are still present.

The shaded right-hand portion of the translated FOV rectangle at the 9o'clock position represents a first sub-portion of the FOV, while theshaded left-hand portion of the FOV rectangle at the 3 o'clock positionrepresents a second sub-portion of the FOV. In the illustratedembodiment, these FOV sub-portions overlap in the central region of theFOV rectangles (though overlap is not necessarily required).

As already mentioned, in some embodiments the first and second axes ofperiodicity in the 2D grating of the MPE region 2050 are not orthogonal.This in turn means that the fundamental grating vectors G and H arelikewise not orthogonal. This can allow the 2D grating in the MPE region2050 to translate the FOV rectangles at the 3 o'clock and 9 o'clockpositions such that the centers of those rectangles lie beyond themidpoint of the k-space annulus, whereas the centers of the FOVrectangles at the 6 o'clock and 12 o'clock positions can be located at,or closer to, the midpoint of the annulus. As a result, the translatedFOV rectangles at the 3 o'clock and 9 o'clock positions are truncated,which results in the FOV being divided into first and secondsub-portions. This is noteworthy in the illustrated embodiment becausedividing the FOV into first and second sub-portions is part of theprocess for increasing the FOV of the eyepiece waveguide 2000.

FIG. 20E is a k-space diagram, KSD3, which illustrates another part ofthe k-space operation of the MPE region 2050 of the eyepiece waveguide2000. KSD3 includes a partially shaded FOV rectangle located at the 3o'clock position of the k-space annulus. This is the location of one ofthe translated FOV rectangles after a first interaction within the MPEregion 2050. FIG. 20E shows how, during subsequent interactions, the 2Dgrating in the MPE region 2050 translates this FOV rectangle using thegrating vectors shown in FIG. 20B. Once again, since there are eightgrating vectors, the MPE region 2050 attempts to translate the FOVrectangle from the 3 o'clock position in the k-space annulus to eightpossible new locations in the k-space diagram. Of these eight possiblelocations, five again fall outside the outer periphery of the k-spacediagram. These locations are illustrated with unshaded FOV rectangles.Since k-vectors outside the outer periphery of the k-space diagram arenot permitted, none of those five grating vectors results indiffraction. There are, however, three grating vectors (i.e., G, H, andH+G) which do result in translations of the FOV rectangle to newpositions at least partially within the bounds of the k-space diagram.One of these locations is at the 9 o'clock position in the k-spaceannulus, another is at the 12 o'clock position, and the last is back atthe 6 o'clock position. Since k-vectors at these locations are permittedand do result in guided propagation modes, the FOV rectangles at theselocations are shaded to indicate that beams of light are diffracted intothose three states (or zero-order diffracted beams can remain in thepropagation state represented by the FOV rectangle at the 3 o'clockposition).

As shown in you FIG. 20E, the translated FOV rectangle at the 3 o'clockposition of the k-space annulus had already been truncated as a resultof the first diffraction interaction in the MPE region 2050 which isshown in FIG. 20D. Thus, only the truncated FOV rectangle is translatedto the 9 o'clock, 12 o'clock, and 6 o'clock positions of the k-spaceannulus. In the case of the 9 o'clock position, the FOV rectangle isfurther truncated, meaning that only the beams corresponding to thecentral shaded portion of that particular translated FOV rectangle areactually diffracted to this state.

FIG. 20F is similar to FIG. 20E, except that it shows the k-spaceoperation of the MPE region 2050 on the FOV rectangle from FIG. 20Dwhich was translated to the 9 o'clock position (instead of the 3 o'clockposition, as illustrated in FIG. 20E). The operation of the MPE region2050 on the beams in this state is a mirror image (about the k_(y)-axis)of what is shown in FIG. 20E.

Although not illustrated, a similar k-space diagram could be drawn toillustrate the k-space operation of the MPE region 2050 on beams oflight traveling with the propagation angles indicated by the FOVrectangle located at the 12 o'clock position of the k-space annulus.That k-space diagram would show that the 2D diffraction grating in theMPE region 2050 would diffract those beams into the states representedby the FOV rectangles at the 3 o'clock, 6 o'clock, and 9 o'clockpositions in the annulus of the k-space diagrams in FIGS. 20D, 20E, and20F.

As shown by the k-space diagrams in FIGS. 20D-20F, when the diffractedlight beams from the ICG region 2040 arrive at the MPE region 2050, manyreplicated beams are formed in a spatially distributed manner. And allof these replicated beams propagate in one of the directions indicatedby the FOV rectangles at the 3 o'clock, 6 o'clock, 9 o'clock, and 12o'clock positions in the k-space annulus. Light beams propagatingthrough the MPE region 2050 may undergo any number of interactions withthe diffractive features of the MPE region, resulting in any number ofchanges in the direction of propagation. In this way, the light beamsare replicated throughout the MPE region 2050 along both the x-directionand the y-direction. This is represented by the arrows in the MPE region2050 of the eyepiece waveguide 2000 in FIG. 20A

Since the EPE region 2060 overlaps the MPE region 2050 within the x-yplane of the eyepiece waveguide 2000, the replicated light beams alsointeract with the EPE region 2060 as they spread through the waveguide,reflecting back and forth between the first surface 2000 a and thesecond surface 2000 b via total internal reflection. When one of thelight beams interacts with the EPE region 2060, a portion of its poweris diffracted and exits the eyepiece waveguide toward the user's eye, asshown by the arrows in the EPE region 2060 of the eyepiece waveguide2000 in FIG. 20A.

In some embodiments, the EPE region 2060 includes a diffraction gratingwhose lines are oriented perpendicularly with respect to the lines ofthe diffraction grating which makes up the ICG region 2040. An exampleof this is shown in FIG. 20A, where the ICG region 2040 has gratinglines which extend in the x-direction, and periodically repeat in they-direction, whereas the EPE region 2060 has grating lines which extendin the y-direction, and periodically repeat in the x-direction. It isadvantageous that the grating lines in the EPE region 2060 are orientedperpendicularly with respect to the grating lines in the ICG region 2040because this helps to ensure that the light beams will interact with theMPE region 2050 before being coupled out of the eyepiece waveguide 2000by the EPE region 2060. This behavior is shown in k-space in FIG. 20G.

FIG. 20G is a k-space diagram, KSD5, which illustrates the k-spaceoperation of the EPE region 2060 in the eyepiece waveguide 2000 shown inFIG. 20A. As already discussed, beams of light propagate through the MPEregion 2050 in all of the directions indicated by the FOV rectangleslocated at the 12 o'clock, 3 o'clock, 6 o'clock, and 9 o'clock positionsof the k-space annulus. And since the EPE region 2060 physicallyoverlaps the MPE region 2050, beams of light in all of these propagationstates come into contact with the diffraction grating in the EPE regionwhile spreading through the MPE region.

Since the axis of periodicity of the diffraction grating in the EPEregion 2060 points in the ±k_(x)-direction, the grating vectorsassociated with the EPE region likewise point in the same direction.FIG. 20G shows how the EPE region 2060 attempts to translate the FOVrectangles at the 12 o'clock, 3 o'clock, 6 o'clock, and 9 o'clockpositions using these grating vectors. Due to their orientation in the±k_(x)-direction, the grating vectors associated with the EPE region2060 can only translate the FOV rectangles located at the 3 o'clock and6 o'clock positions of the k-space annulus back to the origin of thek-space diagram. Thus, the EPE region 2060 can only out-couple beams oflight which are in either of those two propagation states; the EPEregion does not out couple beams of light which are propagating in thestates corresponding to the FOV rectangles at the 12 o'clock and 6o'clock positions of the k-space annulus.

It is important to note that if the axis of periodicity for the gratinglines in the EPE region 2060 were parallel with, rather thanperpendicular to, the axis of periodicity for the grating lines in theICG region 2040, then the grating vectors associated with the EPE regionwould point in the ±k_(y)-direction. This would in turn allow lightbeams in the propagation states corresponding to the FOV rectangles atthe 12 o'clock and 6 o'clock positions of the k-space annulus to be outcoupled by the EPE region. Since input beams arrive at the MPE/EPEregions in the propagation state which corresponds to the 6 o'clockposition, this would mean that light beams could be out-coupled by theEPE region 2060 before interacting with, and being spread by, the MPEregion 2050, which would typically be undesirable. The fact that theaxis of periodicity for the grating lines in the EPE region 2060 isperpendicular to that of the ICG region 2040 means that light beams willtypically need to undergo at least one change of direction, and possiblymany more, within the MPE region before being out coupled. This allowsfor enhanced spreading of the light beams within the MPE region 2050.

FIG. 20H is a k-space diagram, KSD6, which summarizes the k-spaceoperation of the eyepiece waveguide 2000 shown in FIG. 20A. It isessentially a superposition of the k-space diagrams shown in FIGS.20C-20G. Again, the k-space diagram in FIG. 20H shows FOV rectangleshaving at least one dimension that is larger than the width of thek-space annulus. In some embodiments, at least one dimension of the FOVrectangles can be up to approximately 2 times larger than the width ofthe k-space annulus. In the illustrated embodiment, the horizontaldimension of the FOV rectangles is larger than the width of the k-spaceannulus, but the same techniques can also be used to expand the verticalfield of view.

KSD6 includes an FOV rectangle centered at the origin of the diagram.Once again, this location of the FOV rectangle can describe either theinput beams being projected into the eyepiece waveguide 2000 or thereplicated output beams being projected out of the waveguide toward theuser's eye. In the illustrated embodiment, the operation of the ICGregion 2040 in k-space is to translate the FOV rectangle from the centerof the k-space diagram down to the 6 o'clock position. As illustrated,the ICG region 2040 can be designed such that one of its grating vectorsis oriented in the −k_(y)-direction. This causes the diffracted beams topropagate in the −y-direction toward the MPE region 2050. Further, theICG region 2040 can be designed such that the magnitude of its gratingvectors causes the FOV rectangle to be copied to a position where itfits completely within the k-space annulus at the 6 o'clock position.This can be done by, for example, designing the ICG region 2040 with apitch such that the magnitude of its first-order grating vectors isequal to the distance from the origin of the k-space diagram to themidpoint of the k-space annulus. Since the FOV rectangle at the 6o'clock position lies completely within the k-space annulus, all of thediffracted beams enter guided modes of propagation.

As already discussed, the MPE region includes a plurality of diffractivefeatures which exhibit periodicity along multiple different axes. Thismeans that the MPE region has multiple associated grating vectors whichcan translate the FOV rectangle from the 6 o'clock position to any ofthe 9 o'clock, 12 o'clock, and 3 o'clock positions. During additionalinteractions with the MPE region 2050, the FOV rectangles can betranslated back and forth between any of the 12 o'clock, 3 o'clock, 6o'clock, and 9 o'clock positions. This is represented by thedouble-sided arrows between those propagation states. As shown in FIG.20H, the FOV rectangles at the 3 o'clock and 6 o'clock positions of thek-space annulus are truncated, meaning that not all of the beams oflight associated with the full FOV are present in each of thosepropagation states. However, when those sub-portions of the FOV areconsidered collectively, all of the beams of light which make up thefull FOV are present. Thus, when the FOV rectangles are eventuallytranslated from the 3 o'clock or 6 o'clock position back to the originof the k-space diagram, so as to out-couple the beams of light towardthe user's eye, all of the beams which are required to make up the fullFOV of the input image are present and are projected from the eyepiecewaveguide 2000.

FIG. 20I is a diagram which illustrates how beams of light spreadthrough the eyepiece waveguide 2000 shown in FIG. 20A. A guided beamwhich enters the MPE region 2050 propagating in the −y-direction fromthe ICG region 2040 is replicated into many beams in a spatiallydistributed manner, some traveling in the ±y-directions (correspondingto the FOV rectangles at the 6 o'clock and 12 o'clock positions in thek-space annulus), and some traveling in the ±x-directions (correspondingto the FOV rectangles at the 3 o'clock and 9 o'clock positions in thek-space annulus). In this way, light beams spread laterally throughoutthe entire eyepiece waveguide 2000.

FIG. 20J illustrates how the diffractive efficiency of the MPE region2050 in the eyepiece waveguide 2000 can be spatially varied so as toenhance the uniformity of luminance in the waveguide. In the figure,darker shades within the MPE region 2050 represent higher diffractiveefficiency, while lighter shades represent lower diffractive efficiency.The spatial variation in the diffractive efficiency of the MPE region2050 can be accomplished by introducing spatial variation in gratingcharacteristics, such as grating depth, duty cycle, blaze angle, slantangle, etc.

As seen in FIG. 20J, the uniformity of the luminance in the waveguidecan be enhanced by designing portions of the MPE region 2050 which arecloser to the ICG region 2040 to have higher diffractive efficiency.Since this is where light beams enter the MPE region 2050 from the ICGregion 2040, more light is present in this area and thereforediffractive efficiency can be higher here so as to more effectivelyspread the light to other portions of the MPE region 2050 where there isless light. In addition, or alternatively, multiple ICG regions can beprovided at various angular locations around the periphery of the MPEregion 2050 so as to input light at more locations and thereby improveuniformity of luminance in the waveguide.

The uniformity of the luminance can also be enhanced by designing thecentral portion of the MPE region 2050, along the direction in whichbeams propagate from the ICG region 2040 into the MPE region 2050, tohave higher diffractive efficiency. Once again, more light is present inthis area of the MPE region 2050 because it is located along the axiswhere the ICG region 2040 inputs light. Since there is more lightpresent in this area, the diffractive efficiency can be higher so as tomore effectively spread the light to other parts of the MPE region 2050.

FIG. 20K illustrates how the diffractive efficiency of the EPE region2060 in the eyepiece waveguide 2000 can be spatially varied so as toenhance the uniformity of luminance in the waveguide. Darker shadeswithin the EPE region 2060 once again represent higher diffractiveefficiency, while lighter shades represent lower diffractive efficiency.The EPE region 2060 can be designed to have higher diffractiveefficiency in peripheral areas. The higher diffractive efficiency in theperipheral areas of the EPE region 2060 helps to out-couple light to theuser's eye before the light is lost out of the edge of the waveguide.

FIG. 20L illustrates an embodiment of the eyepiece waveguide 2000 whichincludes one or more diffractive mirrors 2070 around the peripheral edgeof the waveguide. The diffractive mirrors 2070 can receive light whichpropagates through the MPE/EPE regions and exits from the edge of thewaveguide 2000. The diffractive mirrors can then diffract that lightback into the MPE/EPE regions so that it can be used to contribute toprojection of the image from the eyepiece waveguide 2000. As alreadydiscussed, the MPE region 2050 permits propagation of beams in fourgeneral directions: generally in the x-direction (i.e., as representedby the FOV rectangle at the 3 o'clock position of the k-space annulus;generally in the −x-direction (i.e., as represented by the FOV rectangleat the 9 o'clock position); generally in the y-direction (i.e., asrepresented by the FOV rectangle at the 12 o'clock position); andgenerally in the −y-direction (i.e., as represented by the FOV rectangleat the 6 o'clock position). The diffractive mirrors 2070 can be designedto diffract beams into one of these same propagation states.

For example, the diffraction mirror 2070 on the left side of theeyepiece waveguide 2000 can diffract beams which are incident generallyfrom the −x-direction into the propagation state represented by the FOVrectangle at the 3 o'clock position such that they travel back throughthe OPE region 2050 generally in the x-direction. Similarly, thediffraction mirror 2070 on the bottom of the eyepiece waveguide 2010 candiffract beams which are incident generally from the −y-direction intothe propagation state represented by the FOV rectangle at the 12 o'clockposition such that they travel back through the OPE region 2050generally in the y-direction.

FIG. 20L illustrates the k-space operation of the bottom diffractivemirror 2070. As shown in the k-space diagram, the bottom diffractivemirror 2070 can be designed with a period that is half that of thegrating in the ICG region 2040. This finer period results in the bottomdiffractive mirror having an associated grating vector which is twice aslong as that of the ICG region 2040. Accordingly, the bottom diffractivemirror can translate the FOV rectangle from the 6 o'clock position inthe k-space annulus to the 12 o'clock position. Although illustratedwith respect to the eyepiece waveguide 2000, the same techniques (i.e.,spatial variation in diffractive efficiency of an OPE, MPE, EPE regionetc., and the usage of diffractive mirrors along peripheral edges) canalso be used with any of the other embodiments described herein.

FIG. 20M illustrates an example embodiment of eyeglasses 70 whichincorporate one or more instances of the eyepiece waveguide 2000. Afirst instance of the eyepiece waveguide 2000 is integrated into theleft viewing portion of the eyeglasses 70, while a second instance ofthe eyepiece waveguide 2000 is integrated into the right viewingportion. In the illustrated embodiment, each of the waveguides 2000 isabout 50×30 mm², though many different sizes can be used. Each waveguide2000 can be accompanied by a separate projector 2020 which projectsimages into the corresponding waveguide. Assuming that the eyepiecewaveguide is made of a material with a refractive index of 1.8, someembodiments of the eyepiece waveguide 2000 are able to achieve an FOV ofas much as 90° by 45°, though some embodiments of the eyepiece waveguidemay be designed for smaller FOVs of −60° by 45° so as to satisfy typicaldesign constraints of eyebox volume—it may be advantageous to send someportion of the FOV to both sides of the eyepiece waveguide to provide anadequately-sized eyebox—and to avoid screen door artifacts resultingfrom sparsely spaced output beams.

FIG. 20N illustrates another example embodiment of eyeglasses 70 whichincorporate one or more instances of the eyepiece waveguide 2000. Thisembodiment of the eyeglasses 70 is similar to that which is shown inFIG. 20M except that the orientation of the waveguides 2000 andaccompanying projectors 2020 have been rotated 90° towards the templesof the eyeglasses 70. In this configuration, some embodiments of theeyepiece waveguide 2000 are able to achieve an FOV of as much as 45° by90°, assuming that the eyepiece waveguide is made of a material with arefractive index of 1.8, though some embodiments may be designed forsmaller FOVs of ˜45° by 60° to satisfy other design constraints.

FIG. 21A illustrates another embodiment of an eyepiece waveguide 2100with an MPE region 2150 which is overlapped by an EPE region 2160.Similar to the eyepiece waveguide 2000 shown in FIG. 20A, the eyepiecewaveguide 2100 shown in FIG. 21A can achieve an expanded field of viewwhich can be larger than the range of propagation angles that can besupported in guided propagation modes in the thickness direction of thewaveguide. The eyepiece waveguide 2100 has a first surface 2100 a and asecond surface 2100 b. As discussed further below, different diffractivefeatures can be formed on or in the opposite surfaces 2100 a, 2100 b ofthe eyepiece waveguide 2100. The two surfaces 2100 a, 2100 b of theeyepiece waveguide 2100 are illustrated in FIG. 21A as being displacedin the x-y plane with respect to one another. However, this is only forpurposes of illustration to be able to show the different diffractivefeatures formed on or in each surface; it should be understood that thefirst surface 2100 a and the second surface 2100 b are aligned with oneanother in the x-y plane. In addition, while the MPE region 2150 and theEPE region 2160 are illustrated as being the same size and exactlyaligned in the x-y plane, in other embodiments they may have somewhatdifferent sizes and may be partially misaligned. In some embodiments,the MPE region 2150 and the EPE region 2160 overlap one another by atleast 70%, at least 80%, at least 90%, or at least 95%.

Like the eyepiece waveguide 2000 shown in FIG. 20A, the eyepiecewaveguide 2100 shown in FIG. 21A includes an MPE region 2150 and an EPEregion 2160. Unlike the eyepiece waveguide 2000 shown in FIG. 20A, theeyepiece waveguide 2100 shown in FIG. 21A includes two ICG regions 2140a, 2140 b, rather than a single ICG region, located on opposite sides ofthe MPE/EPE regions. Each of the ICG regions 2140 a, 2140 b can have itsown associated projector. The two projectors can each input asub-portion of the complete input image FOV into the eyepiece waveguide2100. Accordingly, each of the ICG regions 2140 a, 2140 b can likewisebe used to in-couple input beams corresponding to a sub-portion of theFOV. Those sub-portions can then be combined at the exit pupil of theeyepiece waveguide 2100.

The left ICG region 2140 a receives a first set of input beamscorresponding to a first sub-portion of the FOV from the first projectordevice, while the right ICG region 2140 b receives a second set of inputbeams corresponding to a second sub-portion of the FOV from the secondprojector device. The first and second sub-portions of the FOV may beunique or they may partially overlap. The first set of input beams canbe projected toward the left ICG region 2140 a generally along the−z-direction but centered around an input beam which has a component ofpropagation in the −x-direction, while the second set of input beams canbe projected toward the right ICG region 2140 b generally along the−z-direction but centered around an input beam which has a component ofpropagation in the +x-direction. The left ICG region 2140 a diffractsthe first set of input beams so that at least some enter guided modespropagating in the +x-direction, and the right ICG region 2140 bdiffracts the second set of input beams so that at least some enterguided modes propagating in the −x-direction. In this way, both thefirst and second sets of input beams corresponding to the first andsecond sub-portions of the FOV are coupled into the eyepiece waveguide2100 so that they propagate toward the MPE region 2150 located betweenthe left and right ICG regions 2140 a, 2140 b.

Similar to the eyepiece waveguide 2000 shown in FIG. 20A, the eyepiecewaveguide 2100 shown in FIG. 21A can also include an MPE region 2150which is formed on or in a first side 2100 a of the waveguide and anoverlapping EPE region 2160 which is formed on or in the second side2100 b of the waveguide. The MPE region 2150 in the eyepiece waveguide2100 shown in FIG. 21A can be similar to the MPE region 2050 in theeyepiece waveguide 2000 shown in FIG. 20A. Namely, the MPE region 2150can include a plurality of diffractive features which exhibitperiodicity along multiple axes. Similarly, the EPE region 2160 in theeyepiece waveguide 2100 shown in FIG. 21A can be similar to the EPEregion 2060 in the eyepiece waveguide 2000 shown in FIG. 20A. Namely,the EPE region 2160 can include a diffraction grating whose axis ofperiodicity is orthogonal to that of the two ICG regions 2140 a, 2140 b.The operation of the MPE region 2150 and the EPE region 2160 in FIG. 21Acan also be similar to that of the MPE region 2050 and the EPE region2060 in FIG. 20A, as shown in FIGS. 21B-21D.

FIG. 21B is a k-space diagram, KSD1, which illustrates the k-spaceoperation of the eyepiece waveguide 2100 on the first set of input beamscorresponding to the first sub-portion of the FOV of an input image. TheFOV rectangle centered at the origin of KSD1 represents the beams oflight which correspond to the complete input image FOV that is to beprojected by the eyepiece waveguide 2100 toward the user's eye. The sizeof the FOV rectangle as a whole has a dimension which is up toapproximately two times larger than the width of the k-space annulus.Hence, the eyepiece waveguide 2100 shown in FIG. 21A is designed to havean enhanced FOV similar to the embodiments shown in FIGS. 19 and 20A.However, the first set of input beams which are projected toward theleft ICG region 2140 a correspond to only the shaded sub-portion of theFOV rectangle. As shown in FIG. 21B, the shaded portion of the FOVrectangle which corresponds to the first set of input beams is theleft-hand portion of the FOV rectangle. Since the center of the shadedportion of the FOV rectangle is offset in the −k_(x)-direction from theorigin of the k-space diagram, the first set of input beams from thefirst projector are not centered about a beam propagating exactly in the−z-direction (which would be the case if the shaded portion of the FOVrectangle were centered about the origin of the k-space diagram) butrather about an oblique beam with a propagation component in the−x-direction.

The left ICG region 2140 a can be designed such that its grating vectorsare oriented in the ±k_(x)-direction. The operation of the left ICGregion 2140 a in k-space is to translate the shaded left-hand portion ofthe FOV rectangle from the center of the k-space diagram to the 3o'clock position in the k-space annulus. This will cause the diffractedbeams to propagate generally in the x-direction toward the MPE region2150. In some embodiments, the shaded left-hand portion of the FOVrectangle can constitute half of the FOV rectangle or more. And, in someembodiments, the left ICG region 2140 a can be designed to translate thecenter of the FOV rectangle to any radial position from the midpoint ofthe k-space annulus to the outer boundary of the annulus. Further, theleft ICG region 2140 a can be designed such that the magnitude of itsgrating vectors causes the FOV rectangle to be copied to a positionwhere the shaded portion fits completely within the k-space annulus atthe 3 o'clock position. This can be accomplished by, for example,setting the magnitude of the ICG grating vectors to be greater than thedistance from the origin of the k-space diagram to the midpoint of thek-space annulus. Since the shaded portion of the FOV rectangle at the 3o'clock position lies completely within the k-space annulus, all of thefirst set of input beams corresponding to the first sub-portion of theFOV enter guided modes of propagation. Although the FOV rectangle at the3 o'clock position of the k-space annulus has a right-hand portion whichextends outside the annulus, this portion of the FOV rectanglecorresponds to input beams which are not necessarily part of the firstsub-portion of the FOV provided to the left ICG region 2140 a by itsassociated projector.

Although the left ICG region 2140 a can also diffract a portion of thefirst set of input beams in the opposite direction (i.e., translation ofthe FOV rectangle to the 9 o'clock position of the k-space annulus), inthe illustrated embodiment of the eyepiece waveguide 2100 thoseparticular diffracted beams would simply exit out the edge of thewaveguide.

The MPE region 2150 includes a plurality of diffractive features whichhave multiple axes of periodicity. In some embodiments, the MPE region2150 can be similar to the MPE region 2050 illustrated and discussedwith respect to FIGS. 20A-20M. For example, the MPE region 2150 can havemultiple associated grating vectors which can translate the FOVrectangle from the 3 o'clock position to any of the 6 o'clock, 9o'clock, and 12 o'clock positions of the k-space annulus. As shown inFIG. 21B, the shaded portion of the FOV rectangle at the 9 o'clockposition of the k-space annulus is truncated, meaning that not all ofthe beams of light associated with the first sub-portion of the FOV arenecessarily present in that particular propagation state.

During additional interactions with the MPE region 2150, the FOVrectangles can be translated back and forth between any of the 12o'clock, 3 o'clock, 6 o'clock, and 9 o'clock positions. This isrepresented by the double-sided arrows between those propagation statesin KSD1. In this way, the first set of input beams can be replicatedthroughout the MPE region 2150 by undergoing multiple interactions withits diffractive features, as described herein. This is shown by thearrows in the OPE region 2150 of the eyepiece waveguide 2100 in FIG.21A.

Since the EPE region 2160 overlaps the MPE region 2150 within the x-yplane of the eyepiece waveguide 2100, the replicated light beams alsointeract with the EPE region 2160 as they spread through the waveguide,reflecting back and forth between the first surface 2100 a and thesecond surface 2100 b via total internal reflection. Each time one ofthe replicated light beams interacts with the EPE region 2160, a portionof its power is diffracted and out-coupled toward the user's eye, asshown by the arrows in the EPE region 2160 of the eyepiece waveguide2100 in FIG. 21A.

In some embodiments, the EPE region 2160 includes a diffraction gratingwhose lines are oriented perpendicularly with respect to the lines ofthe diffraction grating which makes up the ICG regions 2140 a, 2140 b.In this particular example, since the ICG regions 2140 a, 2140 b havegrating lines which extend in the y-direction, and periodically repeatin the x-direction, the EPE region 2160 has grating lines which extendin the x-direction, and periodically repeat in the y-direction. Onceagain, it is advantageous that the grating lines in the EPE region 2160are oriented perpendicularly with respect to the grating lines in theICG regions 2140 a 2140 b because this helps to ensure that the lightbeams will interact with the MPE region 2150 before being coupled out ofthe eyepiece waveguide 2100 by the EPE region 2160.

FIG. 21B also illustrates the k-space operation of the EPE region 2160on the first set of beams corresponding to the first sub-portion of theFOV. As already discussed, beams of light can propagate through the MPEregion 2150 in any of the directions indicated by the FOV rectangleslocated at the 12 o'clock, 3 o'clock, 6 o'clock, and 9 o'clock positionsof the k-space annulus. And since the EPE region 2160 overlaps the MPEregion 2150, beams of light in any of these propagation states caninteract with the EPE region and be out-coupled from the eyepiecewaveguide 2100. Since the axes of periodicity of the diffraction gratingin the EPE region 2160 point in the ±k_(y)-direction, the gratingvectors associated with the EPE region likewise point in the samedirection. FIG. 21B shows how the EPE region 2160 therefore translatesthe FOV rectangles located at the 12 o'clock and 6 o'clock positions ofthe k-space annulus back to the origin of the k-space diagram. Thus, theEPE region 2160 can only out couple beams of light which are in eitherof those two propagation states. As shown in FIG. 21B, when the FOVrectangles are eventually translated back to the center of the k-spacediagram KSD1, all of the first set of beams which make up the firstsub-portion of the FOV are present and are projected toward the user'seye.

FIG. 21C is a k-space diagram, KSD2, which illustrates the k-spaceoperation of the eyepiece waveguide 2100 on the second set of inputbeams corresponding to the second sub-portion of the FOV of the inputimage. Once again, the FOV rectangle centered at the origin of KSD2represents the beams of light which correspond to the complete inputimage that is to be projected by the eyepiece waveguide 2100 toward theuser's eye. However, the second set of input beams which are projectedtoward the right ICG region 2140 b correspond to only the shadedsub-portion of the FOV rectangle. As shown in FIG. 21C, the shadedportion of the FOV rectangle which corresponds to the second set ofinput beams is the right-hand portion of the FOV rectangle. Since thecenter of the shaded portion of the FOV rectangle is offset in the+k_(x)-direction from the origin of the k-space diagram, the second setof input beams from the second projector are not centered about a beampropagating exactly in the −z-direction (which would be the case if theshaded portion of the FOV rectangle were centered about the origin ofthe k-space diagram) but rather about an oblique beam with a propagationcomponent in the +x-direction.

In the illustrated embodiment, the operation of the right ICG region2140 b in k-space is to translate the right-hand shaded portion of theFOV rectangle from the center of the k-space diagram to the 9 o'clockposition. As illustrated, the right ICG region 2140 b can be designedsuch that its grating vectors are oriented in the ±k_(x)-direction. Thiswill cause some of the diffracted beams to propagate in the −x-directiontoward the MPE region 2150. In some embodiments, the shaded right-handportion of the FOV rectangle can constitute half of the FOV rectangle ormore. And, in some embodiments, the right ICG region 2140 b can bedesigned to translate the center of the FOV rectangle to any radialposition from the midpoint of the k-space annulus to the outer boundaryof the annulus. Further, the right ICG region 2140 b can be designedsuch that the magnitude of its grating vectors causes the FOV rectangleto be copied to a position where the shaded portion fits completelywithin the k-space annulus at the 9 o'clock position. This can be doneby, for example, designing the ICG such that the magnitude of itsgrating vectors is greater than the distance from the origin of thek-space diagram to the midpoint of the k-space annulus. Since the shadedportion of the FOV rectangle at the 9 o'clock position lies completelywithin the k-space annulus, all of the second set of input beamscorresponding to the second sub-portion of the FOV enter guided modes ofpropagation. Although the FOV rectangle at the 9 o'clock position of thek-space annulus has a left-hand portion which extends outside theannulus, this portion of the FOV rectangle corresponds to input beamswhich are not necessarily part of the second sub-portion of the FOVwhich are projected into the right ICG region 2140 b by its associatedprojector.

Although the right ICG region 2140 b can also diffract a portion of thesecond set of input beams in the opposite direction (i.e., translationof the FOV rectangle to the 3 o'clock position of the k-space annulus),in the illustrated embodiment of the eyepiece waveguide 2100 thoseparticular diffracted beams would simply exit out the edge of thewaveguide.

As already discussed, the MPE region 2150 can have multiple associatedgrating vectors which can translate the FOV rectangle from the 9 o'clockposition to any of the 6 o'clock, 3 o'clock, and 12 o'clock positions ofthe k-space annulus. As shown in FIG. 21C, the shaded portion of the FOVrectangle at the 3 o'clock position of the k-space annulus is truncated,meaning that not all of the beams of light associated with the secondsub-portion of the FOV are necessarily present in that particularpropagation state.

During additional interactions with the MPE region 2150, the FOVrectangles can be translated back and forth between any of the 12o'clock, 3 o'clock, 6 o'clock, and 9 o'clock positions. This isrepresented by the double-sided arrows between those propagation statesin KSD2. In this way, the second set of input beams can be replicatedthroughout the MPE region 2150 by undergoing multiple interactions withits diffractive features, as described herein. Once again, this is shownby the arrows in the OPE region 2150 of the eyepiece waveguide 2100 inFIG. 21A.

FIG. 21C also illustrates the k-space operation of the EPE region 2160on the second set of beams which correspond to the second sub-portion ofthe FOV. As already discussed, the EPE region 2160 translates the FOVrectangles located at the 12 o'clock and 6 o'clock positions of thek-space annulus back to the origin of the k-space diagram. Thus, the EPEregion 2160 can only out-couple beams of light which are in either ofthose two propagation states. As shown in FIG. 21C, when the FOVrectangles are eventually translated back to the center of the k-spacediagram KSD2, all of the second set of beams which make up the secondsub-portion of the FOV are present and are projected toward the user'seye.

FIG. 21D is a k-space diagram, KSD3, which summarizes the k-spaceoperation of the eyepiece waveguide 2100 shown in FIG. 21A. It isessentially a superposition of the k-space diagrams shown in FIGS. 21Band 21C. Again, the k-space diagram in FIG. 21D shows FOV rectangleshaving at least one dimension that is larger than the width of thek-space annulus. In some embodiments, at least one dimension of the FOVrectangles can be up to approximately 2 times larger than the width ofthe k-space annulus. In the illustrated embodiment, the horizontaldimension of the FOV rectangles is larger than the width of the k-spaceannulus. Although the eyepiece waveguide 2100 is illustrated asproviding an expanded horizontal field of view, the same techniques canalso be used to expand the vertical field of view.

As shown in FIG. 21D, although the first and second sets of input beamsare separately projected into the eyepiece waveguide 2100 using separateprojectors and ICG regions 2140 a, 2140 b, once the various FOVrectangles from the 12 o'clock, 3 o'clock, 6 o'clock, and 9 o'clockpositions of the k-space annulus are translated back to the origin ofthe k-space diagram, and are therefore out-coupled toward the user'seye, all of the beams required to make up the complete image FOV arepresent. And the first and second sub-portions of the FOV are aligned ink-space with the same relative positions with respect to one another asin the complete input FOV.

FIG. 21E illustrates an example embodiment of eyeglasses 70 whichincorporate one or more instances of the eyepiece waveguide 2100. FIG.21F illustrates example FOVs corresponding to the eyeglasses 70 in FIG.21E. A first instance of the eyepiece waveguide 2100 is integrated intothe left viewing portion of the eyeglasses 70, while a second instanceof the eyepiece waveguide 2100 is integrated into the right viewingportion. In the illustrated embodiment, each of the eyepiece waveguides2100 is about 50×30 mm², though many different sizes can be used. Eacheyepiece waveguide 2100 can be accompanied by two separate projectors2120 a, 2120 b which each project sub-portions of the FOV into thecorresponding waveguide, as just discussed. In some embodiments, thefirst projector 2120 a for each of the waveguides 2100 can input lighton the temple side of the eyepiece waveguide 2100, while the secondprojector 2120 b can input light on the nasal side of the eyepiecewaveguide. For the case of an eyepiece waveguide made of a materialhaving a refractive index of n=1.8, each of the projectors 2120 a, 2120b can input a sub-portion of the FOV as large as 50° by 60°, or moredepending on other design constraints such as eyebox size and screendoor artifacts. And the complete FOV can be as large as 100° by 60°, ormore. This is shown as the monocular eyepiece FOV configurationillustrated in FIG. 21F. As illustrated by matching shading, in thisconfiguration the first projectors 2120 a (temple side) can be used toproject the nasal side of the complete FOV, and the second projectors2120 b (nasal side) can be used to project the temple side of thecomplete FOV. Note that the cross hair shows one possible pupilalignment, though others can also be used.

Alternatively, the two instances of the eyepiece waveguide 2100 and theeyeglasses 70 can be used jointly to provide a binocular FOV. Forexample, each of the eyepiece waveguides 2100 can project an FOV, asshown in the monocular eyepiece configuration. However, the FOVsprojected by the two eyepiece waveguides 2100 can be at least partiallyoverlapped. FIG. 21F illustrates the case where the FOVs projected bythe two eyepiece waveguides 2100 are overlapped by 50° in the horizontaldirection and provide an overall binocular FOV of 150° by 60°. Thebinocular FOV can be even larger if less overlap is provided between theFOVs of the two eyepiece waveguides 2100. As illustrated by matchingshading, in the binocular FOV configuration, the first projectors 2120 a(temple side) can be used to project the middle portion of the binocularFOV, and the second projectors 2120 b (nasal side) can be used toproject the sides of the binocular FOV.

FIG. 21G illustrates the k-space operation of another embodiment of theeyepiece waveguide 2100 shown in FIG. 21A. In this embodiment, the sizeof the FOV rectangle can exceed the width of the k-space annulus in boththe k_(x) and the k_(y) dimensions. In FIG. 21G, the darker-shadedportions of the FOV rectangles correspond to the right portion of theFOV, while the lighter-shaded portions of the FOV rectangle correspondto the left portion of the FOV. The left and right ICG regions 2140 a,2140 b can be designed with grating vectors to shift the FOV rectanglesto the 3 o'clock and 9 o'clock positions, as already discussed. Themagnitudes of the grating vectors of the ICG regions can be such thatthe center of the complete FOV rectangle is shifted to, for example, anyradial position between the midpoint of the k-space annulus and theouter perimeter of the annulus. And the MPE region can be designed withgrating vectors that shift the complete FOV rectangles to the 3 o'clock,6 o'clock, 9 o'clock and 12 o'clock positions, as already discussed. Butthe magnitudes of the grating vectors of the MPE regions 2150 can alsobe designed such that the center of the complete FOV rectangle isshifted to, for example, any radial position between the midpoint of thek-space annulus and the outer perimeter of the annulus at thoselocations. Accordingly, even at the 12 o'clock and 6 o'clock positions,which are located along the axis of the shorter dimension of the FOVrectangle, a portion of the FOV rectangle may extend beyond the outerperimeter of the k-space annulus such that some portion of the rectangleis truncated.

Although the guided beams which correspond to the truncated portions ofthe FOV rectangles may be lost, all of the beams necessary to make upthe complete FOV are still present in the waveguide when taking intoconsideration all the propagation states represented by the 3 o'clock, 6o'clock, 9 o'clock and 12 o'clock positions. The left FOV(lighter-shaded rectangles) is preserved completely at the 9 o'clockposition, while the bottom portion is preserved at the 12 o'clockposition and the top portion is preserved at the 6 o'clock position.Similarly, the right FOV (darker-shaded rectangles) is preservedcompletely at the 3 o'clock position, while the bottom portion ispreserved at the 12 o'clock position and the top portion is preserved atthe 6 o'clock position. Thus, when the FOV rectangles are translatedback to the origin of the k-space diagram, and are out-coupled towardthe user's eye, all of the beams necessary to make up the complete FOVare present and the complete FOV can be re-created. The expansion of theFOV rectangle in multiple directions is discussed further in FIGS.22A-22E.

FIG. 22A illustrates an embodiment of an eyepiece waveguide 2200 thatcan project an FOV which is expanded in two directions beyond the rangeof propagation angles which can be supported in guided propagation modesin the thickness direction of the eyepiece waveguide. The eyepiecewaveguide 2200 includes a left ICG region 2240 a provided between afirst pair of top and bottom OPE regions 2250 a 1, 2250 a 2. It alsoincludes a right ICG region 2240 b provided between a second pair of topand bottom OPE regions 2250 b 1, 2250 b 2. Finally, an MPE region 2250 cand an overlapping EPE region 2260 are provided between the first andsecond ICG regions 2240 a, 2240 b and their respective OPE regions. TheMPE region 2250 c can be provided on or in a first surface 2200 a of theeyepiece waveguide 2200 (shown in FIG. 22A), while the EPE region 2260can be provided on or in a second surface of the waveguide (shown inFIG. 22B). While the MPE region 2250 c and the EPE region 2260 areillustrated as being the same size and exactly aligned in the x-y plane,in other embodiments they may have somewhat different sizes and may bepartially misaligned. In some embodiments, the MPE region 2250 c and theEPE region 2260 overlap one another by at least 70%, at least 80%, atleast 90%, or at least 95%.

The left ICG region 2240 a and the first pair of top and bottom OPEregions 2250 a 1, 2250 a 2 function similarly to what has been shown anddescribed with respect to FIG. 19. Namely, a projector or other inputdevice projects a set of beams corresponding to an input image FOVtoward the left ICG region 2240 a generally along the −z-direction. Theleft ICG region 2240 a has grating lines which extend in the x-directionand periodically repeat in the y-direction. The left ICG region 2240 atherefore couples input beams of light into a +1 diffractive order and a−1 diffractive order which propagate generally in the +y-directiontoward the upper OPE region 2250 a 1 and in the −y-direction toward thelower OPE region 2250 a 2. The first set of upper and lower OPE regions2250 a 1, 2250 a 2 replicate those input beams, as discussed herein, andthen guide the sets of replicated output beams generally in thex-direction toward the MPE/EPE regions.

The right ICG region 2240 b and the second pair of top and bottom OPEregions 2250 a 1, 2250 a 2 function in the same way, but mirrored aboutthe y-axis. Namely, a projector or other input device projects the sameset of input beams toward the right ICG region 2240 b generally alongthe −z-direction. The right ICG region 2240 b also has grating lineswhich extend in the x-direction and periodically repeat in they-direction. The right ICG region 2240 b therefore also couples inputbeams of light into a +1 diffractive order and a −1 diffractive orderwhich propagate generally in the +y-direction toward the upper OPEregion 2250 b 1 and in the −y-direction toward the lower OPE region 2250b 2. The second set of upper and lower OPE regions 2250 b 1, 2250 b 2replicate those input beams and then guide the sets of replicated outputbeams generally in the −x-direction toward the MPE/EPE regions.

FIG. 22C illustrates the k-space operation of the ICG regions 2240 a,2240 b and the OPE regions 2250 a 1, 2250 a 2, 2250 b 1, 2250 b 2 in theeyepiece waveguide embodiment 2200 shown in FIG. 22A. Specifically, theleft panel (KSD1 a) of FIG. 22C illustrates the k-space operation of theleft ICG region 2240 a and its associated first set of top and bottomOPE regions 2250 a 1, 2250 a 2, while the right panel (KSD1 b) of FIG.22C illustrates the k-space operation of the right ICG region 2240 b andits associated second set of top and bottom OPE regions 2250 b 1, 2250 b2.

A set of input beams corresponding to the FOV of an input image isprojected toward both the left ICG region 2240 a and the right ICGregion 2240 b. This set of input beams is illustrated in KSD1 a and KSD1b as an FOV square centered at the respective origins of these k-spacediagrams. Unlike previous illustrated enhanced FOV embodiments whichshowed only a single dimension of the FOV being larger than the width ofthe k-space annulus, both dimensions of the FOV square in KSD1 a andKSD1 b are larger than the width of the k-space annulus. In someembodiments, both dimensions of the FOV square can be up toapproximately 2 times larger than the width of the k-space annulus.Although this embodiment is illustrated using an FOV square with equalhorizontal and vertical FOVs, this is not a requirement, as thehorizontal and vertical FOVs need not necessarily be equal. Embodimentsof the eyepiece waveguide 2200 shown in FIG. 22A may be capable ofachieving FOVs as large as 100° by 60°, or more (e.g., 100° by 90°)depending on other design constraints such as eyebox size and screendoor artifacts, assuming an eyepiece waveguide (surrounded by air) withrefractive index 1.8.

In KSD1 a, the FOV square is translated in the ±k_(y)-direction ink-space by the grating vectors associated with the left ICG region 2240a. Similarly, in KSD1 b, the FOV square is translated in the±k_(y)-direction in k-space by the grating vectors associated with theright ICG region 2240 b. In both cases, after being in-coupled into theeyepiece waveguide 2200 by the ICG regions 2240 a, 2240 b, the inputbeams are in propagation states represented by the translated FOVsquares at the 12 o'clock and 6 o'clock positions of the k-spaceannulus. As shown in both KSD1 a and KSD1 b, the FOV squares in thesepositions are truncated because they do not fit entirely within thek-space annulus. Only those beams corresponding to the shaded lowerportion of the FOV square at the 12 o'clock position enter guidedpropagation modes. Meanwhile, only those beams corresponding to theshaded upper portion of the FOV square at the 6 o'clock position enterguided propagation modes.

KSD1 a also shows the k-space operation of the first set of top andbottom OPE regions 2250 a 1, 2250 a 2. These OPE regions includediffraction gratings which are designed to have associated gratingvectors which translate the FOV squares from the 12 o'clock and 6o'clock positions to the 3 o'clock position. Beams in the 3 o'clockposition propagate generally in the x-direction toward the MPE/EPEregions.

The beams corresponding to the upper portion of the FOV square at the 3o'clock position in k-space are provided by the FOV square which waspreviously located at the 6 o'clock position, whereas the beamscorresponding to the lower portion of the FOV square at the 3 o'clockposition are provided by the FOV square which was previously located atthe 12 o'clock position. However, the FOV square is once again too largeto fit entirely within the k-space annulus at the 3 o'clock position.The FOV square is therefore truncated, but this time the beamscorresponding to the shaded left-hand portion of the FOV square remainin guided propagation modes, whereas the beams corresponding to theunshaded right-hand portion of the FOV square fall outside the k-spaceannulus and are lost.

The k-space operation of the second set of top and bottom OPE regions2250 b 1, 2250 b 2 is a mirrored version (about the k_(y)-axis) of thek-space operation of the first set of top and bottom OPE regions 2250 a1, 2250 a 2. Thus, as shown in KSD1 b, the second set of top and bottomOPE regions 2250 b 1, 2250 b 2 ultimately produce a truncated FOV squareat the 9 o'clock position of the k-space annulus where the beamscorresponding to the shaded right-hand portion of the square propagatein guided modes toward the MPE/EPE regions, while the beamscorresponding to the unshaded left-hand portion of the FOV square falloutside the k-space annulus and are lost.

FIG. 22D illustrates the k-space operation of the MPE region 2250 c inthe eyepiece waveguide embodiment 2200 shown in FIG. 22A. Specifically,the left panel (KSD2 a) of FIG. 22D illustrates the k-space operation ofthe MPE region 2250 c on the beams received from the left ICG region2240 a and its associated first set of top and bottom OPE regions 2250 a1, 2250 a 2, while the right panel (KSD2 b) illustrates the k-spaceoperation of the MPE region 2250 c on the beams received from the rightICG region 2240 b and its associated second set of top and bottom OPEregions 2250 b 1, 2250 b 2.

The MPE region 2250 c can operate similarly to what has been describedwith respect to the MPE regions 2050, 2150 in FIGS. 20A and 21A. Namely,as already discussed, the MPE region 2250 c can be composed of a 2Darray of diffractive features which exhibit periodicity in multipledirections. The MPE region 2250 c therefore has multiple associatedgrating vectors which can translate FOV square back and forth amongstthe 3 o'clock, 6 o'clock, 9 o'clock, and 12 o'clock positions of thek-space annulus. This is represented by the double-sided arrows betweenthose propagation states in KSD2 a and KSD2 b. In this embodiment, thegrating vectors G and H of the MPE region 2250 c can be perpendicular toone another because the FOV is expanded beyond the width of the k-spaceannulus in both dimensions, and therefore the center of the FOV squarecan be translated to the same radial locations in the k-space annulus inboth the k_(x) and k_(y) directions.

As already discussed, the beams which arrive at the MPE region 2250 cfrom the left ICG region 2240 a and the first set of top and bottom OPEregions 2250 a 1, 2250 a 2 are in the propagation state represented bythe FOV square at the 3 o'clock position of the k-space annulus. Onlythe beams corresponding to the shaded left-hand portion of the FOVsquare are present in this propagation state. As shown in KSD2 a, whenthe MPE region 2250 c diffracts these beams into the propagation staterepresented by the FOV square at the 12 o'clock position, the FOV squareis once again truncated and only the beams corresponding to the shadedlower left portion of the FOV square remain in guided propagationstates. Meanwhile, when the MPE region 2250 c diffracts beams from thepropagation state represented by the FOV square at the 3 o'clockposition into the propagation state represented by the FOV square at the6 o'clock position, the FOV square is also truncated again; only thebeams corresponding to the shaded upper left portion of the FOV squareremain in guided propagation states. Finally, when the FOV squares aretranslated from either the 12 o'clock position or the 6 o'clock positionof the k-space annulus to the 9 o'clock position, the FOV square is yetagain truncated, which may possibly not leave any of the beams in guidedpropagation states. This is shown by the unshaded FOV square at the 9o'clock position in KSD2 a.

KSD2 b is a mirror image of KSD2 a about the k_(y)-axis. KSD2 b showsthe k-space operation of the MPE region 2250 c on the beams of lightwhich arrive from the right ICG region 2240 b and the second set of topand bottom OPE regions 2250 b 1, 2250 b 2. These beams are in thepropagation state represented by the FOV square at the 9 o'clockposition of the k-space annulus. Only the beams corresponding to theshaded right-hand portion of the FOV square are present in thispropagation state. As shown in KSD2 b, when the MPE region 2250 cdiffracts these beams into the propagation state represented by the FOVsquare at the 12 o'clock position, the FOV square is once againtruncated and only the beams corresponding to the shaded lower rightportion of the FOV square remain in guided propagation states.Meanwhile, when the MPE region 2250 c diffracts beams from thepropagation state represented by the FOV square at the 9 o'clockposition into the propagation state represented by the FOV square at the6 o'clock position, the FOV square is also truncated again; only thebeams corresponding to the shaded upper right portion of the FOV squareremain in guided propagation states. Finally, when the FOV squares aretranslated from either the 12 o'clock position or the 6 o'clock positionof the k-space annulus to the 3 o'clock position, the FOV square is yetagain truncated, which may possibly not leave any of the beams in guidedpropagation states. This is shown by the unshaded FOV square at the 3o'clock position in KSD2 b.

In this way, the beams which are replicated by propagation through theMPE region 2250 c are divided into four sub-portions of the FOV: a firstsub-portion corresponding to the upper left portion of the FOV square; asecond sub-portion corresponding to the upper right portion of the FOVsquare; a third sub-portion corresponding to the lower left portion ofthe FOV square; and a fourth sub-portion corresponding to the lowerright portion of the FOV square. Any pair of these sub-portions of thecomplete FOV can be partially overlapping. In other words, any pair ofthese sub-portions of the FOV can include beams which correspond to oneor more of the same input beams. Alternatively, the sub-portions of theFOV could also be unique with no overlap. In either case, thesub-portions of the FOV are combined to re-create the complete FOV atthe exit pupil of the eyepiece waveguide 2200. This is shown in FIG.22E.

FIG. 22E illustrates the k-space operation of the EPE region 2260 in theeyepiece waveguide embodiment 2200 shown in FIG. 22A. The EPE region2260 can function similarly to what has been described with respect tothe EPE regions 2060, 2160 in FIGS. 20A and 21A. As discussed herein,since the EPE region 2260 overlaps the MPE region 2250 c, beams of lightpropagating in the MPE region can also interact with the EPE region andbe out-coupled from the eyepiece waveguide 2200. The EPE region 2260includes a diffraction grating whose axis of periodicity is aligned withthose of the left ICT region 2240 a and the right ICG region 2240 b. Inthe illustrated embodiment, the axis of periodicity for the EPE region2260 points in the ±k_(y)-direction. The EPE region 2260 therefore hasassociated grating vectors which likewise point in the same directionand translate the FOV squares located at the 12 o'clock and 6 o'clockpositions of the k-space annulus back to the origin of the k-spacediagram. FIG. 22E shows that when this occurs, the four sub-portions ofthe FOV are assembled to re-create the complete FOV. All of the beamsrequired to make up the complete image FOV are present. And the foursub-portions of the FOV are aligned in k-space with the same relativepositions with respect to one another as in the complete input FOV.

Eyepiece Waveguides Designed to Work with Angled Projectors

Many of the eyepiece waveguide embodiments described herein have beendesigned to work with a projector (or other image input device) whoseoptical axis intersects the ICG region at a perpendicular angle. In suchembodiments, the center input beam (which corresponds to the centerpoint of the input image) is perpendicularly incident on the ICG region,and the input beams corresponding to the top/bottom and left/rightportions of the input image are incident on the ICG region atsymmetrical angles. In some embodiments, however, an eyepiece waveguidemay be designed to function with an angled projector (or other imageinput device). FIG. 23 illustrates an example of such an embodiment.

FIG. 23 illustrates an example embodiment of an eyepiece waveguide 2300designed to function with an angled projector. The eyepiece waveguide2300 includes an ICG region 2340, left and right OPE regions 2350 a,2350 b, and an EPE region 2360. Input beams from a projector areincident on the ICG region 2340 and are coupled into the eyepiecewaveguide 2300 in guided propagation modes. In this embodiment, theprojector is oriented at a non-perpendicular angle with respect to theICG region 2340. The center input beam 2341 from the projector istherefore incident on the ICG region 2340 at an oblique angle (e.g., asillustrated in FIG. 13I). This results in a shift in k-space of thek-vectors for the input beams, causing them to no longer be centeredabout the origin of a k-space diagram. As a result, the optical designof the ICG, OPE, and/or EPE regions may need to be altered, along withtheir physical shape (e.g., according to the principles described withreference to FIG. 14D), and the placement of FOV rectangles in thek-space annulus may also change, as discussed below.

The positive and negative diffractive orders from the ICG region 2340then propagate to the left and right OPE regions 2350 a, 2350 b,respectively. The OPE regions 2350 replicate the input beams in aspatially distributed manner in the horizontal direction and direct themtoward the EPE region 2360. The EPE region 2360 then further replicatesthe beams in a spatially distributed manner in the vertical directionand out couples them toward the user's eye, as discussed elsewhereherein.

FIG. 23 includes a k-space diagram, KSD, which illustrates the k-spaceoperation of the eyepiece waveguide 2300. As described elsewhere herein,the FOV rectangle in the central portion of the k-space diagramcorresponds to the input beams from the projector and the output beamsfrom the eyepiece waveguide 2300. The FOV rectangles near the 4 o'clockand 8 o'clock positions in the k-space annulus correspond to the beamsof light propagating from the ICG region 2340 to the OPE regions 2350.Lastly, the FOV rectangle at the 6 o'clock position in the k-spaceannulus corresponds to the beams of light propagating from the OPEregions 2350 downward toward the EPE region 2360.

Since the projector is angled with respect to the ICG region 2340, theFOV rectangle corresponding to the input beams is not centered at theorigin of the k-space diagram. Instead, in the illustrated embodiment,the FOV rectangle corresponding to the input beams is centered on thek_(g)-axis but located below the k_(x)-axis. This means that none of theinput beams have propagation directions with components in the+y-direction. In other words, the input beams propagate downward fromthe projector toward the ICG region. The ICG region 2340 then translatesthe FOV rectangle horizontally into the k-space annulus in the±k_(x)-directions.

Since none of the guided light beams from the ICG region 2340 havek-vectors with a positive k_(y) component (i.e., the FOV rectangles arelocated below the k_(x)-axis), the top edges of the OPE regions 2350 canbe horizontal, as illustrated, since there is no need to accommodatebeams of light fanning out upwardly in the +y-direction. Thischaracteristic of the OPE regions 2350 may be advantageous in someembodiments because it may allow for a compact design. However, thehorizontal top edge of the OPE regions 2350 is made practical by theangled image projector. The angled image projector may, however, beassociated with some disadvantages. For example, since the eyepiecewaveguide 2300 (including, for example, the optical design and/orphysical layout of gratings) is designed to receive input light from anupward angle, light from overhead sources, such as the sun or overheadlight fixtures, may likewise be coupled into the eyepiece waveguide.This may result in undesirable image features, such as ghost images ofthose light sources superimposed on the displayed virtual content,artifacts, reduced contrast, etc. Although light from overhead sourcesmay be blocked by including a visor so as to shade the eyepiecewaveguide 2300 from overhead light, such a visor may be bulky oraesthetically undesirable. Thus, eyepiece waveguides which are designedto function with perpendicular projectors may be preferred because theneed for a visor can be reduced or eliminated. In addition, for upwardor downward angled projector designs, the fact that output beams alsoexit the waveguide at an angle similar to the input beams means that theeyepiece waveguide may need to be tilted relative to the user's centralgaze vector and/or it may need to be placed above or below—rather thandirectly in front of—the eye.

Example AR Eyepiece Waveguides with Combined Pupil Expander-ExtractorRegions

FIG. 24A is an edge view of an example eyepiece waveguide 2400 that hasmultiple combined pupil expander-extractor (CPE) regions 2455. The CPEregions 2455 take the place of the OPE, MPE, and/or EPE regions whichare described herein with respect to other embodiments. The illustratedembodiment has first and second CPE regions 2455 a, 2455 b on opposingsides of the eyepiece waveguide 2400. The first and second CPE regions2455 a, 2455 b both spread light laterally inside the eyepiece waveguide2400, similar to an OPE region. They also both extract the light fromthe eyepiece waveguide 2400, similar to an EPE region.

The eyepiece waveguide 2400 shown in FIG. 24A can be formed using asubstrate made of an optically transmissive material. The eyepiecewaveguide 2400 has an eye-facing side 2400 a and an outward-facing side2400 b. In the illustrated embodiment of the eyepiece waveguide 2400, anICG region 2440 is provided at the top center of the eyepiece waveguide2400, and the first and second CPE regions 2455 a, 2455 b are providedbelow the ICG region 2440 on the eye-facing side 2400 a and theoutward-facing side 2400 b, respectively.

In some embodiments, the ICG region 2440 is a diffraction grating formedon or in a surface of the eyepiece waveguide 2400 (e.g., on theeye-facing side 2400 a). The ICG region 2440 receives a set of inputbeams from an input device, such as a projector. As described elsewhereherein, the input beams can propagate from the input device generally inthe ±z-direction until they are incident upon the ICG region 2440. TheICG region 2440 diffracts those input beams so that at least some enterguided propagation modes within the eyepiece waveguide 2400.

The illustrated embodiment of the diffraction grating inside the ICGregion 2440 has one-dimensional periodicity (i.e., it is a 1D grating).The grating lines of the ICG region 2040 can be oriented so as to directsome of the diffracted beams in the −y-direction toward the first andsecond CPE regions 2455 a, 2455 b. Thus, in the illustrated embodiment,the ICG region 2440 includes diffractive lines which extend in the±x-direction and repeat periodically in the ±y-direction. As describedelsewhere herein, the spacing between the diffractive lines which makeup the ICG region 2440 can be set so as to couple the input beams oflight into guided propagation modes inside the eyepiece waveguide 2400.The diffracted beams from the ICG region 2440 then propagate via TIRtoward the first and second CPE regions 2455 a, 2455 b.

The first CPE region 2455 a is formed on or in one side of the eyepiecewaveguide (e.g., the eye-facing side 2400 a) and the second CPE region2455 b is formed on or in the opposite side of the eyepiece waveguide(e.g., the outward-facing side 2400 b). In the illustrated embodiment,the first and second CPE regions 2455 a, 2455 b are both 1D diffractiongratings. The first CPE region 2455 a is illustrated as a 1D diffractiongrating made up of diffractive lines oriented at an angle of −30° withrespect to the y-axis (when viewed from the eye-facing side 2400 a), andthe second CPE region 2455 b is illustrated as a 1D diffraction gratingmade up of diffractive lines oriented at an angle of +30° with respectto the y-axis (when also viewed from the eye-facing side 2400 b).

In some embodiments of the eyepiece waveguide 2400, the relative anglebetween the 1D grating of the first CPE region 2455 a and the 1D gratingof the second CPE region 2455 b is substantially 60° (i.e., 60°±5°, or60°±3°, or 60°±1°, or 60°±0.5°, or 60° ±0.1°. In addition, in someembodiments, the relative angles between the 1D grating of the ICGregion 2440 and the 1D gratings of both of the CPE regions 2455 a, 2455b are also substantially 60° (i.e., 60°±5°, or 60°±3°, or 60°±1°, or60°±0.5°, or 60°±0.1°. Other layouts for the eyepiece waveguide 2400besides the specific example shown in FIG. 24A are also possible. Forexample, the ICG region 2440 could instead be located on the temporal ormedial side of the eyepiece waveguide 2400 and the orientations of theCPE regions 2455 a, 2455 b could be adjusted accordingly to maintain therelative angles between gratings.

As discussed further below, the relative angle of substantially 60°between each of the respective 1D gratings of the ICG region 2440, thefirst CPE region 2455 a, and the second CPE region 2455 b contributes tothe characteristic that the CPE regions can both laterally spread lightin the eyepiece waveguide 2400 and out-couple light towards the user'seye.

In some embodiments, the 1D gratings of the first and second CPE regions2455 a, 2455 b are identical apart from their orientations. For example,the first and second CPE regions 2455 a, 2455 b can have the same linespacing, the same etch depth, etc. This can be advantageous because itpermits both CPE regions 2455 to be manufactured from the same mastertemplate. In addition, in some embodiments, the 1D grating of the ICGregion 2440 also has the same line spacing as the first and second CPEregions 2455 a, 2455 b.

While the first CPE region 2455 a and the second CPE region 2455 b areillustrated as being the same size and exactly aligned in the x-y plane,in other embodiments they may have somewhat different sizes and/or theymay be partially misaligned. In some embodiments, the first and secondCPE regions 2455 a, 2455 b overlap one another by at least 70%, or by atleast 80%, or by at least 90%, or by at least 95%.

As already mentioned, the guided beams of light from the ICG region 2440propagate through the eyepiece waveguide 2400 via TIR, meaning theyreflect back and forth between the respective surfaces of the eye-facingside 2400 a and the outward-facing side 2400 b. As the guided beamspropagate through the eyepiece waveguide 2400 in this manner, theyalternately interact with the diffraction gratings of the first andsecond CPE regions 2455 a, 2455 b. The operation of the first and secondCPE regions 2455 a, 2455 b on the guided beams of light is discussedfurther with respect to FIGS. 24B-24K.

FIG. 24B illustrates the operation of the first and second CPE regions2455 a, 2455 b in both physical space and in k-space according to afirst type of main pathway of light through the eyepiece waveguide 2400.A physical diagram of the eyepiece waveguide 2400 is shown on the lefthand side of FIG. 24B. The eyepiece waveguide 2400 is shown as viewedfrom the eye-facing side 2400 a. A k-space diagram, KSD1 a, of theoperation of the ICG region 2440 and the first and second CPE regions2455 a, 2455 b is shown on the right hand side of FIG. 24B.

As already discussed, a set of input beams is incident on the ICG region2440 of the eyepiece waveguide 2400 from an input device, such as aprojector. This set of input beams is represented by the FOV rectangleshown in the center of k-space diagram KSD1 a. The diffraction gratingin the ICG region 2440 has associated positive and negative gratingvectors which point in the ±k_(y)-directions. Thus, the k-spaceoperation of the ICG region 2440 is to shift the central FOV rectangleto both the six o'clock and 12 o'clock positions on k-space diagram KSD1a. (The FOV rectangle at the 12 o'clock position corresponds to lightbeams propagating in the +y-direction. Since those beams exit theeyepiece waveguide 2400 out of its top edge, that particular FOVrectangle is not illustrated and those beams are not discussed further.)The length of the grating vectors associated with the ICG region 2440can be set, based on the spacing of the diffractive lines and thewavelength of the light, such that the translated FOV rectangle at thesix o'clock position lies completely within the k-space annulus.

For ease of illustration, the physical diagram on the left hand side ofFIG. 24B only shows one of the guided beams of light from the ICG region2440 (i.e., guided beam 2441 corresponding to the center k-vector in theFOV rectangle located at the six o'clock position of the k-space diagramKSD1 a). Guided beam 2441 from the ICG region 2440 propagates downwardthrough the eyepiece waveguide 2400 in the −y-direction, reflecting backand forth in TIR between the surface of the eye-facing side 2400 a andthe surface of the outward-facing side 2400 b. Each time guided beam2441 reflects from the eye-facing side 2400 a, it can interact with thefirst CPE region 2455 a. And each time guided beam 2441 reflects fromthe outward facing side 2400 b, it can interact with the second CPEregion 2455 b. The diffractive efficiency of the first and second CPEregions 2455 a, 2455 b can be set so that only a portion of the power ofeach beam of light is diffracted with each of these interactions. Forexample, in some embodiments, the diffractive efficiency of the firstand second CPE regions 2455 a, 2455 b is 10% or less. The diffractiveefficiency of the first and second CPE regions 2455 a, 2455 b can bedetermined by, for example, the etch depth of the diffractive lines.

The physical diagram on the left hand side of FIG. 24B shows theinteractions of guided beam 2441 with the first CPE region 2455 a whichcause light to spread laterally in the −x-direction through the eyepiecewaveguide 2400. As guided beam 2441 propagates downward in the−y-direction through the eyepiece waveguide 2400, a portion of its poweris diffracted at a +120° angle with respect to the y-axis during eachinteraction with the first CPE region 2455 a. The remaining portion ofthe power of guided beam 2441 continues propagating downward in the−y-direction until the next interaction with the first CPE region 2455a, where another portion of its power is diffracted at the same +120°angle. This process creates a plurality of spaced apart diffracted beams2456 a which propagate through the eyepiece waveguide 2400 at a +120°angle with respect to the y-axis. These diffracted beams 2456 a arerepresented by the FOV rectangle located at the 8 o'clock position ink-space diagram KSD1 a on the right hand side of FIG. 24B.

As with any 1D diffraction grating, there are positive and negativegrating vectors associated with the first CPE region 2455 a. Thesegrating vectors point along the direction of periodicity of the gratinglines in the first CPE region 2455 a. Accordingly, one of thefirst-order grating vectors associated with the first CPE region 2455 apoints at +60° with respect to the y-axis (as shown in KSD1 a), whilethe other points in the opposite direction at −120° with respect to they-axis. The same is true for the positive and negative higher-ordergrating vectors. The first-order grating vector which points at +60°with respect to the y-axis shifts the FOV rectangle from the six o'clockposition (which corresponds to the downward propagating guided beamsfrom the ICG region 2440) to the eight o'clock position (whichcorresponds to the diffracted beams 2456 a propagating at the +120°angle with respect to the y-axis). (The first-order grating vector whichpoints at −120° with respect to the y-axis would shift the FOV rectanglefrom the six o'clock position to a location outside of the k-spaceannulus and therefore does not result in diffraction.)

Once guided beams from the ICG region 2440 interact with the first CPEregion 2455 a and are diffracted into the propagation states representedby the FOV rectangle at the eight o'clock position of k-space diagramKSD1 a, they then interact with the second CPE region 2455 b on the nextTIR bounce as they are guided through the eyepiece waveguide 2400. Theinteraction of these beams 2456 a with the second CPE region 2455 b canresult in them being out-coupled from the eyepiece waveguide 2400 towardthe user's eye. The out-coupled beams 2457 a are shown in the physicaldiagram of the eyepiece waveguide 2400 on the left hand side of FIG. 24Bas circled dots, indicating that those beams are propagating in thez-direction out of the page. The out-coupling of beams 2456 a by thesecond CPE region 2455 b can be understood by reference to k-spacediagram KSD1 a.

Just as there are positive and negative grating vectors associated withthe first CPE region 2455 a, there are also positive and negativegrating vectors associated with the second CPE region 2455 b. Thesegrating vectors point along the direction of periodicity of the gratinglines in the second CPE region 2455 b. Accordingly, one of thefirst-order grating vectors associated with the second CPE region 2455 bpoints at −60° with respect to the y-axis (as shown in KSD1 a), whilethe other points in the opposite direction at +120° with respect to they-axis. The same is true for the positive and negative higher-ordergrating vectors. The first-order grating vector which points at −60°with respect to the y-axis shifts the FOV rectangle from the eighto'clock position (which corresponds to the diffracted beams 2456 apropagating at a +120° angle with respect to the y-axis) to the centerof k-space diagram KSD1 a (which corresponds to out-coupled beams oflight which are no longer in guided propagation modes inside theeyepiece waveguide 2400). (The first-order grating vector which pointsat +120° with respect to the y-axis would shift the FOV rectangle fromthe eight o'clock position to a location outside of the k-space annulusand therefore does not result in diffraction.)

The physical diagram on the left hand side of FIG. 24B shows how theinteractions of light beams 2456 a with the second CPE region 2455 bresults in multiple spaced-apart out-coupled beams 2457 a. As lightbeams 2456 a propagate at the +120° angle with respect to the y-axis, aportion of their power is out-coupled by each interaction with thesecond CPE region 2455 b. The remaining portion of the power of lightbeams 2456 a continues propagating at the +120° angle with respect tothe y-axis until the next interaction with the second CPE region 2455 b,where another portion of the power of those beams is out-coupled. Thisprocess creates a plurality of spaced-apart out-coupled beams 2457 awhich exit the eyepiece waveguide 2400 at different spatial locationsand propagate toward the user's eye. As already noted, these out-coupledbeams 2457 a are represented by the FOV rectangle located at the centerof k-space diagram KSD1 a.

The passage of beams of light through the eyepiece waveguide 2400 in themanner shown in k-space diagram KSD1 a in FIG. 24B is the first type ofmain pathway of light through the eyepiece waveguide. There is also asecond type of main pathway of light through the eyepiece waveguide 2400which is illustrated by k-space diagram KSD1 b in FIG. 24C.

FIG. 24C illustrates the operation of the first and second CPE regions2455 a, 2455 b in both physical space and in k-space according to thesecond type of main pathway of light through the eyepiece waveguide2400. Once again, a physical diagram of the eyepiece waveguide 2400 isshown on the left hand side of FIG. 24C. The eyepiece waveguide 2400 isagain shown as viewed from the eye-facing side 2400 a. A k-spacediagram, KSD1 b, of the operation of the ICG region 2440 and the firstand second CPE regions 2455 a, 2455 b is shown on the right hand side ofFIG. 24C.

The physical diagram on the left hand side of FIG. 24C shows the sameguided beam 2441 from the ICG region 2440 as is shown in FIG. 24B. Butthis time, the physical diagram shows the interactions of guided beam2441 with the second CPE region 2455 b which cause light to laterallyspread in the +x-direction through the eyepiece waveguide 2400. Namely,as guided beam 2441 propagates downward in the −y-direction through theeyepiece waveguide 2400, a portion of its power is diffracted at asubstantially −120° angle with respect to the y-axis during eachinteraction with the second CPE region 2455 b. The remaining portion ofthe power of guided beam 2441 continues propagating downward in the−y-direction until the next interaction with the second CPE region 2455b, where another portion of its power is diffracted at the same −120°angle. This process creates a plurality of spaced apart diffracted beams2456 b which propagate through the eyepiece waveguide 2400 at a −120°angle with respect to the y-axis. These diffracted beams 2456 b arerepresented by the FOV rectangle located at the 4 o'clock position ink-space diagram KSD1 b on the right hand side of FIG. 24C.

As already discussed, one of the first-order grating vectors associatedwith the second CPE region 2455 b points at −60° with respect to they-axis (as shown in KSD1 b), while the other points in the oppositedirection at +120° with respect to the y-axis. The first-order gratingvector which points at −60° with respect to the y-axis shifts the FOVrectangle from the six o'clock position (which corresponds to thedownward propagating guided beams from the ICG region 2440) to the fouro'clock position (which corresponds to the diffracted beams 2456 bpropagating at the −120° angle with respect to the y-axis). (Thefirst-order grating vector which points at +120° with respect to they-axis would shift the FOV rectangle from the six o'clock position to alocation outside of the k-space annulus and therefore does not result indiffraction.)

Once guided beams from the ICG region 2440 interact with the second CPEregion 2455 b and are diffracted into the propagation states representedby the FOV rectangle at the four o'clock position of k-space diagramKSD1 b, they then interact with the first CPE region 2455 a on the nextTIR bounce as they are guided through the eyepiece waveguide 2400. Theinteraction of these beams 2456 b with the first CPE region 2455 a canresult in them being out-coupled from the eyepiece waveguide 2400 towardthe user's eye. The out-coupled beams 2457 b are shown in the physicaldiagram of the eyepiece waveguide 2400 on the left hand side of FIG. 24Cas circled dots, indicating that those beams are propagating in thez-direction out of the page. The out-coupling of beams 2456 b by thefirst CPE region 2455 a can be understood by reference to k-spacediagram KSD1 b.

As already discussed, one of the first-order grating vectors associatedwith the first CPE region 2455 a points at +60° with respect to they-axis (as shown in KSD1 b), while the other points in the oppositedirection at −120° with respect to the y-axis. The first-order gratingvector which points at +60° with respect to the y-axis shifts the FOVrectangle from the four o'clock position (which corresponds to thediffracted beams 2456 b propagating at a −120° angle with respect to they-axis) to the center of k-space diagram KSD1 a (which corresponds toout-coupled beams of light which are no longer in guided propagationmodes inside the eyepiece waveguide 2400). (The first-order gratingvector which points at −120° with respect to the y-axis would shift theFOV rectangle from the four o'clock position to a location outside ofthe k-space annulus and therefore does not result in diffraction.)

The physical diagram on the left hand side of FIG. 24C shows how theinteractions of light beams 2456 b with the first CPE region 2455 aresults in multiple spaced-apart out-coupled beams 2457 b. As lightbeams 2456 b propagate at the −120° angle with respect to the y-axis, aportion of their power is out-coupled by each interaction with the firstCPE region 2455 a. The remaining portion of the power of light beams2456 b continues propagating at the −120° angle with respect to they-axis until the next interaction with the first CPE region 2455 a,where another portion of the power of those beams is out-coupled. Thisprocess creates a plurality of spaced-apart out-coupled beams 2457 bwhich exit the eyepiece waveguide 2400 at different spatial locationsand propagate toward the user's eye. As already noted, these out-coupledbeams 2457 b are represented by the FOV rectangle located at the centerof k-space diagram KSD1 b.

FIG. 24D illustrates the operation of the first and second CPE regions2455 a, 2455 b in both physical space and in k-space according to boththe first and second types of main pathways of light through theeyepiece waveguide 2400. Yet again, a physical diagram of the eyepiecewaveguide 2400 is shown on the left hand side of FIG. 24D. The eyepiecewaveguide 2400 is again shown as viewed from the eye-facing side 2400 a.A k-space diagram, KSD2, of the operation of the ICG region 2440 and thefirst and second CPE regions 2455 a, 2455 b is shown on the right handside of FIG. 24D.

As already discussed, both types of main pathways of light through theeyepiece waveguide 2400 begin with a set of input lightbeams—corresponding to an input image—which are incident on the ICGregion 2440. The set of input light beams is represented by the FOVrectangle located at the center of k-space diagram KSD2. The ICG region2440 couples the input light beams into guided propagation modes withinthe eyepiece waveguide 2400. This is represented by the translation ofthe FOV rectangle—by one of the first-order grating vectors associatedwith the ICG region—from the center of k-space diagram KSD2 to the 6o'clock position of the k-space annulus. The physical diagram on theleft hand side of FIG. 24D shows a single one of the resulting guidedbeams (i.e., guided beam 2441). It should be understood, however, thatmany guided input beams will be present, each of which will correspondto a different k-vector inside the FOV rectangle located at the 6o'clock position in the k-space annulus of KSD2.

The guided light beams from the ICG region 2440 then have multiplealternating interactions with the first and second CPE regions 2455 a,2455 b as they TIR between the surface of the eye-facing side 2400 a ofthe eyepiece waveguide 2400 and the surface of the outward-facing side2400 b. During each generation of interactions, a portion of the powerof each of the beams can zero-order diffract and continue propagating inthe same direction in the x-y plane of the eyepiece waveguide 2400,while another portion of the power of each of the beams can first-orderdiffract into a new propagation direction.

Some of the light beams in the propagation states represented by the FOVrectangle at the 6 o'clock position in KSD2 will first interact with thefirst CPE region 2455 a, while others will first interact with thesecond CPE region 2455 b. In the case of those light beams whose initialinteraction is with the first CPE region 2455 a, a portion of the powerof each of those beams will first-order diffract, thereby creatingdiffracted beams of light (e.g., diffracted beams 2456 a) whosepropagation states are represented by the FOV rectangle at the 8 o'clockposition of the k-space annulus in KSD2, and another portion of thepower of each of those beams will zero-order diffract resulting indiffracted beams of light whose propagation states continue to berepresented by the FOV rectangle at the 6 o'clock position. All of thosebeams of light will then interact with the second CPE region 2455 b onthe subsequent TIR bounce as they propagate through the eyepiecewaveguide 2400.

During the interaction with the second CPE region 2455 b, a portion ofthe power of the beams whose propagation states are represented by theFOV rectangle at the 8 o'clock position will first-order diffract,thereby creating out-coupled beams of light (e.g., beams 2457 a) whosepropagation states are represented by the FOV rectangle at the center ofthe k-space annulus in KSD2, and another portion of the power of each ofthose beams will zero-order diffract resulting in beams of light (e.g.,beams 2456 a) whose propagation states continue to be represented by theFOV rectangle at the 8 o'clock position. Meanwhile, a portion of thepower of the beams whose propagation states are represented by the FOVrectangle at the 6 o'clock position will follow the second type of mainpathway through the eyepiece waveguide 2400. Namely, a portion of thepower of the beams whose propagation states are represented by the FOVrectangle at the 6 o'clock position will first-order diffract in theinteraction with the second CPE region 2455 b, thereby creating beams oflight (e.g., beams 2456 b) whose propagation states are represented bythe FOV rectangle at the 4 o'clock position of the k-space annulus inKSD2, and another portion of the power of each of those beams willzero-order diffract resulting in beams of light whose propagation statescontinue to be represented by the FOV rectangle at the 6 o'clockposition. All of those beams of light will then interact with the firstCPE region 2455 a on the subsequent TIR bounce as they propagate throughthe eyepiece waveguide 2400.

During the next interaction with the first CPE region 2455 a, a portionof the power of the beams whose propagation states are represented bythe FOV rectangle at the 4 o'clock position will first-order diffract,thereby creating out-coupled beams of light (e.g., beams 2457 b) whosepropagation states are represented by the FOV rectangle at the center ofthe k-space annulus in KSD2, and another portion of the power of each ofthose beams will zero-order diffract resulting in beams of light (e.g.,beams 2456 b) whose propagation states continue to be represented by theFOV rectangle at the 4 o'clock position. Meanwhile, a portion of thepower of the beams whose propagation states are represented by the FOVrectangle at the 6 o'clock position will follow the first type of mainpathway through the eyepiece waveguide 2400. Namely, a portion of thepower of the beams whose propagation states are represented by the FOVrectangle at the 6 o'clock position will first-order diffract in theinteraction with the first CPE region 2455 a, thereby creating beams oflight (e.g., beams 2456 a) whose propagation states are represented bythe FOV rectangle at the 8 o'clock position of the k-space annulus inKSD2, and another portion of the power of each of those beams willzero-order diffract resulting in beams of light whose propagation statescontinue to be represented by the FOV rectangle at the 6 o'clockposition. All of those beams of light will then interact with the secondCPE region 2455 b on the subsequent TIR bounce as they propagate throughthe eyepiece waveguide 2400 and the cycle will repeat.

As is evident from the k-space diagrams in FIGS. 24B-24D, the 1Ddiffraction gratings in the ICG region 2440, the first CPE region 2455a, and the second CPE region 2455 b can be oriented such that theirassociated grating vectors are all at substantially 60° angles withrespect to one another. In addition, the 1D diffraction gratings in theICG region 2440, the first CPE region 2455 a, and the second CPE region2455 b can all have the same line spacing such that their associatedgrating vectors all have the same magnitude. These properties, incombination with the fact that the first and second CPE regions 2455 a,2455 b are on opposite sides of the eyepiece waveguide 2400, andtherefore light beams alternately interact with those gratings, causeslight beams to propagate along paths in k-space which are defined byequilateral triangles. These equilateral triangular paths allow thefirst and second CPE regions 2455 a, 2455 b to both spread lightlaterally in the eyepiece waveguide 2400 and to both out-couple lightfrom the eyepiece waveguide to the user's eye.

FIG. 24E is a diagram of the first generation of interactions between aninput beam and the CPE regions 2455 of the eyepiece waveguide embodimentshown in FIG. 24A. In the illustrated case, the first generation ofinteractions is with the first CPE region 2455 a, though it couldalternatively be with the second CPE region 2455 b. FIG. 24E shows aguided input beam that enters the first CPE region 2455 a from the ICGregion 2440. The input beam is shown propagating in a direction whichcorresponds to one of the k-vectors in the FOV rectangle located at the6 o'clock position of the k-space annulus in FIGS. 24B-24D. In someembodiments, the input beam has a diameter of ˜5 mm or less, or of ˜1 mmor less.

At every interaction with the first CPE region 2455 a, the input beamwill split into 2 beams (each with the same diameter but a fraction ofthe original power of the input beam) propagating in 2 differentdirections in TIR. One direction corresponds to zero-order diffractionand is the original propagation angle in the x-y plane of the eyepiecewaveguide 2400. The other direction depends on the grating vectorsassociated with the first CPE region 2455 a. As shown, the firstgeneration of interactions between the input beam and the first CPEregion 2455 a results in two beams: some portion of the power of theinput beam simply reflects, as output₁, from the surface of the eyepiecewaveguide 2400 and continues on in the same x-y direction as the inputbeam (i.e., the 0^(th) order diffraction); and some portion of the powerof the input beam interacts with the 1D grating in the first CPE region2455 a and is diffracted as output₂. The output₂ beam is shownpropagating in a direction which corresponds to one of the k-vectors inthe FOV rectangle located at the 8 o'clock position of the k-spaceannulus in FIGS. 24B-24D. After this first generation of interactions,the output₁ beam and the output₂ beam may subsequently interact with thesecond CPE region 2455 b. Although not illustrated, other guided inputbeams that enter the first CPE region 2455 a from the ICG region 2440with different propagation angles will behave similarly but withslightly different input and output angles.

FIG. 24F is a diagram of the second generation of interactions betweenthe input beam and the CPE regions 2455 of the eyepiece waveguideembodiment shown in FIG. 24A. In the illustrated case, the secondgeneration of interactions is with the second CPE region 2455 b. Thebeams related to the first generation of interactions are shown withdashed lines, while the beams related to the second generation ofinteractions are shown with solid lines. As shown in FIG. 24F, each ofthe output beams, output₁ and output₂, from the first generation ofinteractions can now interact with the second CPE region 2455 b. Someportion of the power of the output₁ beam from FIG. 24E zero-orderdiffracts and continues on in the same x-y direction (corresponding toone of the k-vectors in the FOV rectangle at the 6 o'clock position ofthe k-space diagrams in FIGS. 24B-24D), while another portion of thepower of that beam interacts with the grating in the second CPE region2455 b and is first-order diffracted in a direction corresponding to oneof the k-vectors in the FOV rectangle located at the 4 o'clock positionof the k-space diagrams in FIGS. 24B-24D. Similarly, some portion of thepower of the output₂ beam from FIG. 24E zero-order diffracts andcontinues on in the same direction (corresponding to one of thek-vectors in the FOV rectangle located at the 8 o'clock position of thek-space diagrams in FIGS. 24B-24D), while another portion of the powerof that beam interacts with the grating in the second CPE region 2455 band is first-order diffracted and out-coupled from the eyepiecewaveguide 2400. After this second generation of interactions, theoutput₁ beams and the output₂ beam may subsequently interact with thefirst CPE region 2455 a.

FIG. 24G is a diagram of the third generation of interactions betweenthe input beam and the CPE regions of the eyepiece waveguide embodimentshown in FIG. 24A. In the illustrated case, the third generation ofinteractions is with the first CPE region 2455 a. The beams related tothe first and second generations of interactions are shown with dashedlines, while the beams related to the third generation of interactionsare shown with solid lines. As shown in FIG. 24G, each of the outputbeams, output₁ and output₂, from the second generation of interactionscan now interact with the first CPE region 2455 a. Some portion of thepower of the output₁ beam from FIG. 24F which belongs to the FOVrectangle located at the 8 o'clock position of the k-space annuluszero-order diffracts and continues on in the same x-y direction, whileanother portion of the power of that beam is first-order diffracted in adirection corresponding to one of the k-vectors in the FOV rectanglelocated at the 6 o'clock position. Some portion of the power of theoutput₁ beam from FIG. 24F which belongs to the FOV rectangle located atthe 6 o'clock position of the k-space annulus zero-order diffracts andcontinues on in the same x-y direction, while another portion of thepower of that beam is first-order diffracted in a directioncorresponding to one of the k-vectors in the FOV rectangle located atthe 8 o'clock position. Finally, some portion of the power of theoutput₂ beam from FIG. 24F zero-order diffracts and continues on in thesame x-y direction, while another portion of the power of that beam isfirst-order diffracted and out-coupled from the eyepiece waveguide 2400.After this third generation of interactions, the output₁ beams and theoutput₂ beams may subsequently interact with the second CPE region 2455b.

FIG. 24H is a diagram of the fourth generation of interactions betweenthe input beam and the CPE regions 2455 of the eyepiece waveguideembodiment shown in FIG. 24A. In the illustrated case, the fourthgeneration of interactions is with the second CPE region 2455 b. Thebeams related to the first, second, and third generations ofinteractions are shown with dashed lines, while the beams related to thefourth generation of interactions are shown with solid lines. In thisgeneration of interactions, some of the beams of light are out-coupledfrom the eyepiece waveguide 2400 and each of the others is diffractedinto a direction corresponding to a k-vector which belongs to one of theFOV rectangles at the 4 o'clock, 6 o'clock, or 8 o'clock positions inthe k-space annulus of the k-space diagrams in FIGS. 24B-24D. After thisfourth generation of interactions, the output₁ beams and the output₂beams may subsequently interact with the first CPE region 2455 a.

FIG. 24I is a diagram of the fifth generation of interactions betweenthe input beam and the CPE regions 2455 of the eyepiece waveguideembodiment shown in FIG. 24A. In the illustrated case, the fifthgeneration of interactions is with the first CPE region 2455 a. Thebeams related to the first, second, third, and fourth generations ofinteractions are shown with dashed lines, while the beams related to thefifth generation of interactions are shown with solid lines. As in theprevious generations of interactions, some of the beams of light areout-coupled from the eyepiece waveguide 2400 and each of the others isdiffracted into a direction corresponding to a k-vector which belongs toone of the FOV rectangles at the 4 o'clock, 6 o'clock, or 8 o'clockpositions in the k-space annulus of the k-space diagrams in FIGS.24B-24D. After this fifth generation of interactions, the output₁ beamsand the output₂ beams may subsequently interact with the second CPEregion 2455 b and the cycle continues to repeat.

FIG. 24J illustrates, in k-space, higher-order pathways of light throughthe eyepiece waveguide 2400 shown in FIG. 24A. The k-space diagrams inFIGS. 24B-24D show the first-order grating vectors associated with theICG region 2440 and the CPE regions 2455. The first-order gratingvectors result in guided propagation modes represented by the FOVrectangles at the 4 o'clock, 6 o'clock, and 8 o'clock positions in thek-space annulus. However, each of the CPE 2455 regions is alsoassociated with positive and negative second-order grating vectors, someof which also result in guided propagation modes.

As already discussed herein, second-order grating vectors point in thesame directions as the corresponding first-order grating vectors buthave twice the magnitude. Thus, as shown in FIG. 24J, light beams in thepropagation modes represented by the FOV rectangle at the 4 o'clockposition in the k-space annulus can be second-order diffracted by thefirst CPE region 2455 a into propagation modes represented by the FOVrectangle at the 10 o'clock position of the k-space annulus. Similarly,light beams in the propagation modes represented by the FOV rectangle atthe 8 o'clock position in the k-space annulus can be second-orderdiffracted by the second CPE region 2455 b into propagation modesrepresented by the FOV rectangle at the 2 o'clock position of thek-space annulus. From the 2 o'clock and 10 o'clock positions,first-order diffractions by the CPE regions 2455 can result in lightbeams in the propagation modes represented by the FOV rectangle at the12 o'clock position.

The propagation modes at the 10 o'clock, 12 o'clock, and 2 o'clockpositions in the k-space annulus, which are associated with second-orderdiffractions paths, can still be out-coupled to the user's eye. Forexample, light beams in the propagation modes represented by the FOVrectangle at the 10 o'clock position in the k-space annulus can befirst-order diffracted by the first CPE region 2455 a as out-coupledbeams represented by the FOV rectangle at the center of the k-spaceannulus. Similarly, light beams in the propagation modes represented bythe FOV rectangle at the 2 o'clock position in the k-space annulus canbe first-order diffracted by the second CPE region 2455 b as out-coupledbeams represented by the FOV rectangle at the center of the k-spaceannulus.

FIG. 24K is a diagram which illustrates how beams of light spreadthrough the eyepiece waveguide 2400 shown in FIG. 24A. A guided beamwhich enters the CPE regions 2455 propagating in the −y-direction fromthe ICG region 2440 is replicated into many beams, some traveling in the±y-directions (corresponding to the FOV rectangles at the 6 o'clock and12 o'clock positions in the k-space annulus), some traveling at ±60°with respect to the y-axis (corresponding to the FOV rectangles at the 2o'clock and 10 o'clock positions in the k-space annulus), and sometraveling at ±120° with respect to the y-axis (corresponding to the FOVrectangles at the 4 o'clock and 8 o'clock positions in the k-spaceannulus). In this way, light beams spread laterally throughout theentire eyepiece waveguide 2400.

FIG. 25A is an edge view of an example eyepiece waveguide 2500 that hasa single 2D combined pupil expander-extractor (CPE) grating region 2555.The single 2D CPE region 2555 operates in a manner similar to thecombined operation of the two 1D CPE regions 2455 a, 2455 b shown inFIG. 24A. For example, the CPE region 2555 spreads light laterallyinside the eyepiece waveguide 2500, similar to an OPE region, and italso extracts the light from the eyepiece waveguide 2500, similar to anEPE region.

Although the single 2D CPE region 2555 in FIG. 25A operates in a similarfashion as the two 1D CPE regions 2455 a, 2455 b in FIG. 24A docollectively, it has a distinct structure in that it is made up ofdiffractive features that exhibit periodicity in two or more directions,whereas each of the 1D CPE regions 2455 a, 2455 b in FIG. 24A is made upof diffractive features with periodicity in a single direction. Sincethe 2D CPE region 2555 in FIG. 25A can perform the operations that arecollectively performed by the two 1D CPE regions 2455 a, 2455 b in FIG.24A, it can be formed on or in a single side of the eyepiece waveguide2500, whereas the CPE regions 2455 a, 2455 b in FIG. 24A arerespectively formed on or in both sides of the eyepiece waveguide 2400.

The fact that the CPE region 2555 in FIG. 25A is a single-sided 2Ddesign—as opposed to the double-sided 1D design of FIG. 24A—may beadvantageous in terms of fabrication, as an eyepiece waveguide (e.g.,2500) with gratings on only one side may be less complicated tomanufacture than an eyepiece waveguide (e.g., 2400) with gratings onboth sides. For example, manufacture of the double-sided design of FIG.24A may involve procedures to obtain precise angular alignment ofgrating 2455 a with respect to grating 2455 b on the opposite side,whereas manufacturer of the single-sided design of FIG. 25A may omitthose angular alignment procedures. Some embodiments of the single-sideddesign in FIG. 25A may also offer certain advantages in opticalperformance because there is no risk of angular misalignment—and thedegraded optical performance that can result therefrom—between gratingson opposite sides of the eyepiece waveguide.

The eyepiece waveguide 2500 shown in FIG. 25A can be formed using asubstrate made of an optically transmissive material. The eyepiecewaveguide 2500 has an eye-facing side 2500 a and an outward-facing side2500 b. In the illustrated embodiment of the eyepiece waveguide 2500, anICG region 2540 is provided at the top center of the eyepiece waveguide2500, and the CPE region 2555 is provided below the ICG region 2540 onthe eye-facing side 2400 a. However, other configurations are possible.For example, the CPE region 2555 and/or the ICG region 2540 mayalternatively be provided on the outward-facing side 2500 b of theeyepiece waveguide 2500 so that the ICG and CPE regions act inreflection or transmission modes. In addition, as in other embodiments,the ICG region could be positioned at other locations, such as thetemporal or medial side of the eyepiece waveguide 2500.

In some embodiments, the ICG region 2540 is a diffraction grating formedon or in a surface of the eyepiece waveguide 2500 (e.g., on theeye-facing side 2500 a). The ICG region 2540 receives a set of inputbeams from an input device, such as a projector. As described elsewhereherein, the input beams can propagate from the input device generally inthe ±z-direction until they are incident upon the ICG region 2540. TheICG region 2540 diffracts those input beams so that at least some enterguided propagation modes within the eyepiece waveguide 2500.

The illustrated embodiment of the diffraction grating inside the ICGregion 2540 has one-dimensional periodicity (i.e., it is a 1D grating).The grating lines of the ICG region 2540 can be oriented so as to directsome of the diffracted beams in the −y-direction toward the CPE region2555. Thus, in the illustrated embodiment, the ICG region 2540 includesdiffractive lines which extend in the ±x-direction and repeatperiodically in the ±y-direction. As described elsewhere herein, thespacing between the diffractive lines which make up the ICG region 2540can be set so as to couple the input beams of light into guidedpropagation modes inside the eyepiece waveguide 2500. The diffractedbeams from the ICG region 2540 then propagate via TIR toward the CPEregion 2555.

The CPE region 2555 in FIG. 25A has two-dimensional periodicity (i.e.,it is a 2D grating). The 2D grating 2555 has a corresponding set ofk-space grating vectors that includes the grating vectors of both of theCPE regions 2455 a, 2455 b in the design of FIGS. 24A-24K. In someembodiments, the CPE region 2555 in FIG. 25A consists of a crossedgrating created by superposition of CPE region 2455 a and CPE region2455 b from FIGS. 24A-24K. In some embodiments, the CPE region 2555 inFIG. 25A consists of an array of diffractive features located at (e.g.,centered on) the intersection points 2556 where the line gratings of CPEregion 2455 a and CPE region 2455 b would cross if superimposed.

As already discussed above, CPE region 2455 a in FIGS. 24A-24K can be a1D diffraction grating made up of diffractive lines oriented at an angleof −30° with respect to the y-axis. This 1D grating corresponds to ak-space grating vector that is labeled as grating vector G in FIG. 25B.Meanwhile, CPE region 2455 b can be a 1D diffraction grating made up ofdiffractive lines oriented at an angle of +30° with respect to they-axis. This 1D grating corresponds to a k-space grating vector that islabeled as grating vector H in FIG. 25B. The relative angle between the1D grating of CPE region 2455 a and the 1D grating of CPE region 2455 b,and between each of those gratings and the 1D grating of the ICG region2440, is substantially 60° (i.e., 60°±5°, or 60°±3°, or 60°±1°, or60°±0.5°, or 60°±0.1°. Thus, the k-space grating vectors G, H for theCPE regions 2455 a, 2455 b in FIGS. 24A-24K are likewise oriented atsubstantially 60° with respect to one another. The 2D grating of CPEregion 2555 in FIG. 25A likewise has these same first-order gratingvectors G and H (in addition to higher-order grating vectorscorresponding to the sums of ±G and ±H).

Besides being oriented at substantially 60° with respect to one another,the first-order grating vectors G, H of the 2D grating of the CPE region2555 are also oriented at substantially 60° with respect to the gratingvector of the ICG region 2540. Furthermore, the 2D grating of the CPEregion 2555 can be designed with spatial periodicities such that itsfirst-order grating vectors G, H are substantially equal in magnitude tothe first-order grating vector of the ICG region 2540. The operation ofthe CPE region 2555 on the guided beams of light from the ICG region2540 is described with respect to FIG. 25B.

FIG. 25B illustrates the operation of the 2D CPE region 2555 in bothphysical space and in k-space. A physical diagram of the eyepiecewaveguide 2500 is shown at the top of FIG. 25B. A k-space diagram, KSD1,of the operation of the ICG region 2540 and the CPE region 2555 is shownat the bottom of FIG. 25B.

As already discussed, a set of input beams is incident on the ICG region2540 of the eyepiece waveguide 2500 from an input device, such as aprojector. This set of input beams is represented by the FOV rectangleshown in the center of k-space diagram KSD1. The diffraction grating inthe ICG region 2540 has associated positive and negative grating vectorswhich point in the ±k_(y)-directions. Thus, the k-space operation of theICG region 2540 is to shift the central FOV rectangle to both the sixo'clock and 12 o'clock positions on k-space diagram KSD1. (The FOVrectangle at the 12 o'clock position corresponds to light beamspropagating in the +y-direction. Since those beams exit the eyepiecewaveguide 2500 out of its top edge, that particular FOV rectangle is notillustrated and those beams are not discussed further.) The length ofthe ICG grating vector can be set, based on the spacing of thediffractive lines and the wavelength of the light, such that thetranslated FOV rectangle at the six o'clock position lies completelywithin the k-space annulus.

For ease of illustration, the physical diagram at the top of FIG. 25Bonly shows one of the guided beams of light from the ICG region 2540(i.e., guided beam 2541 corresponding to the center k-vector in the FOVrectangle located at the six o'clock position of the k-space diagramKSD1). It should be understood, however, that many guided input beamswill be present, each of which will correspond to a different k-vectorinside the FOV rectangle located at the 6 o'clock position in thek-space annulus of KSD1.

Guided beam 2541 from the ICG region 2540 propagates downward throughthe eyepiece waveguide 2500 in the −y-direction, reflecting back andforth in TIR between the surface of the eye-facing side 2500 a and thesurface of the outward-facing side 2500 b. Each time guided beam 2541reflects from the eye-facing side 2500 a, it can interact with the CPEregion 2555. The diffractive efficiency of the CPE region 2555 can beset so that only a portion of the power of each beam of light isdiffracted with each of these interactions. For example, in someembodiments, the diffractive efficiency of the CPE region 2555 is 10% orless. The diffractive efficiency of the CPE region 2555 can bedetermined by, for example, the etch depth of the diffractive features.For example, in some embodiments, the heights of the diffractivefeatures can range from about 5 nm up to about 200 nm. In someembodiments, the heights of the diffractive features can range from justgreater than zero up to a half wavelength of guided beam 2541.

The physical diagram at the top of FIG. 25B shows the interactions ofguided beam 2541 with the CPE region 2555 which cause light to spreadlaterally in both of the ±x-directions through the eyepiece waveguide2500. As guided beam 2541 propagates downward in the −y-directionthrough the eyepiece waveguide 2500, portions of its power arediffracted at ±120° angles with respect to the y-axis during eachinteraction with the CPE region 2555. The remaining portion of the powerof guided beam 2541 continues propagating downward in the −y-directionuntil the next interaction with the CPE region 2555, where portions ofits power are again diffracted at the same ±120° angles. This processcreates a plurality of spaced apart diffracted beams 2556 a, 2556 bwhich propagate through the eyepiece waveguide 2500 at a +120° angle anda −120° angle, respectively, with respect to the y-axis. Diffractedbeams 2556 a, propagating at the +120° angle, are represented by the FOVrectangle located at the 8 o'clock position in k-space diagram KSD1,while diffracted beams 2556 b, propagating at the −120° angle, arerepresented by the FOV rectangle located at the 4 o'clock position.

With reference to k-space diagram KSD1 at the bottom of FIG. 25B, thefirst-order grating vector G, which points at +60° with respect to thek_(y)-axis, shifts the FOV rectangle from the six o'clock position(which corresponds to the downward propagating guided beams from the ICGregion 2540) to the eight o'clock position (which corresponds to thediffracted beams 2556 a propagating at the +120° angle with respect tothe y-axis). Similarly, the first-order grating vector H, which pointsat −60° with respect to the k_(y)-axis, shifts the FOV rectangle fromthe six o'clock position (which corresponds to the downward propagatingguided beams from the ICG region 2540) to the 4 o'clock position (whichcorresponds to the diffracted beams 2556 b propagating at the −120°angle with respect to the y-axis).

Once guided beams from the ICG region 2540 interact with the CPE region2555 and are diffracted into the propagation states represented by theFOV rectangles at the 4 o'clock and eight o'clock positions of k-spacediagram KSD1, they then interact again with the CPE region 2555 on asubsequent TIR bounce as they are guided through the eyepiece waveguide2500. This subsequent interaction of beams 2556 a and 2556 b with theCPE region 2555 can result in them being out-coupled from the eyepiecewaveguide 2500 toward the user's eye. The out-coupled beams 2557 areshown in the physical diagram of the eyepiece waveguide 2500 at the topof FIG. 25B as circled dots, indicating that those beams are propagatingin the z-direction out of the page. The out-coupling of beams 2556 a,2556 b by the CPE region 2555 can be understood by reference to k-spacediagram KSD1.

The first-order grating vector H, which points at −60° with respect tothe y-axis, shifts the FOV rectangle from the eight o'clock position(which corresponds to the diffracted beams 2556 a propagating at a +120°angle with respect to the y-axis) to the center of k-space diagram KSD1(which corresponds to out-coupled beams of light 2557 which are nolonger in guided propagation modes inside the eyepiece waveguide 2500).Similarly, the first-order grating vector G, which points at +60° withrespect to the y-axis, shifts the FOV rectangle from the four o'clockposition (which corresponds to the diffracted beams 2556 b propagatingat a −120° angle with respect to the y-axis) to the center of k-spacediagram KSD1 (which corresponds to out-coupled beams of light 2557 whichare no longer in guided propagation modes inside the eyepiece waveguide2500).

The physical diagram at the top of FIG. 25B shows how the subsequentinteractions of light beams 2556 a, 2556 b with the CPE region 2555results in multiple spaced-apart out-coupled beams 2557. As light beams2556 a, 2556 b propagate at the ±120° angles with respect to the y-axis,portions of their power are out-coupled by each subsequent interactionwith the CPE region 2555. The remaining portions of the power of lightbeams 2556 a, 2556 b continue propagating at the ±120° angles withrespect to the y-axis until the next interaction with the CPE region2555, where another portion of the power of those beams is out-coupled.This process creates a plurality of spaced-apart out-coupled beams 2557which exit the eyepiece waveguide 2500 at different spatial locationsand propagate toward the user's eye. As already noted, these out-coupledbeams 2557 are represented by the FOV rectangle located at the center ofk-space diagram KSD1.

In addition, although not illustrated in FIG. 25B, light can also spreadthrough the eyepiece waveguide 2500 in the manner shown in FIG. 24J.That is, due to higher-order diffractions, light can also spread indirections represented by FOV rectangles at 2 o'clock, 10 o'clock, and12 o'clock positions of the k-space annulus.

As shown in k-space diagram KSD1 in FIG. 25B, light beams propagatethrough the eyepiece waveguide 2500 along paths in k-space which aresubstantially similar to equilateral triangles. Thesesubstantially-equilateral triangular paths allow the CPE region 2555 toboth spread light laterally in the eyepiece waveguide 2500 and toout-couple light from the eyepiece waveguide to the user's eye.

FIG. 26A is an edge view of an example eyepiece waveguide 2600 that hasa 2D combined pupil expander-extractor (CPE) grating region 2655 on eachof its sides. Each of the 2D CPE regions 2655 a, 2655 b can be similarto the 2D CPE region 2555 of FIGS. 25A-25B. For example, CPE region 2655a can be an instance of CPE region 2555 located on the eye-facing side2600 a of the eyepiece waveguide 2600, while CPE region 2655 b can be aninstance of CPE region 2555 located on the outward-facing side 2600 b.The two 2D CPE regions 2655 a, 2655 b can partially or wholly overlap inthe x- and y-directions, and can be angularly aligned with one another.The double-sided embodiment with 2D CPE regions 2655 on both sides ofthe eyepiece waveguide functions similarly to the single-sidedembodiment of FIGS. 25A-25B. In k-space, the operation of thedouble-sided embodiment of FIG. 26A is the same as that of thesingle-sided embodiment in FIG. 25A. However, the double-sidedembodiment does increase the density of output beams as compared to thesingle-sided embodiment. The increased density of output beams can beuseful in addressing the design complications shown in FIGS. 26B and26C.

FIG. 26B illustrates the so-called “screen door effect” which is animage artifact that is related to the density of output beams from aneyepiece waveguide. The top panel in FIG. 26B shows an eyepiecewaveguide 2600 with a diffraction grating on the top surface. A guidedlight beam 2656 is shown propagating through the eyepiece waveguide viaTIR. At the location of each interaction of the guided light beam 2656with the diffraction grating, an output beam 2657 is out-coupled fromthe eyepiece waveguide 2600. If the entrance pupil of the user's eyehappens to be aligned with one of the output beams 2657, as shown in thetop panel of FIG. 26B, then the user will see a bright spot. (Note: therespective dimensions of the eyepiece waveguide 2600, the light beams2656, 2657, and the entrance pupil of the eye are not necessarily drawnto scale.)

The bottom panel of FIG. 26B shows the same eyepiece waveguide 2600, butthis time the guided beam 2656 and the output beams 2657 correspond to adifferent region of the field of view of the output image beingdisplayed. The output beams 2657 therefore exit the eyepiece waveguideat a different angle such that the entrance pupil of the user's eye isnot aligned with any of the output beams 2657. In this instance, theuser will see a dark spot.

As the density of the output beams 2657 increases, so does thelikelihood that one or more will always intersect with the entrancepupil of the eye, for all regions of the FOV of the output image.Therefore, eyepiece waveguide designs with higher densities of outputbeams 2657 may be advantageous.

The severity of the screen door effect is dependent on multiple factors,including the diameter of the light beams and the thickness of theeyepiece waveguide 2600. One technique for increasing the density of theoutput beams 2657 is to decrease the thickness of the eyepiecewaveguide. As is evident from FIG. 26B, if the thickness of the eyepiecewaveguide 2600 were smaller, the guided beam 2656 would travel a shorterdistance in the x-direction between interactions with the diffractiongrating and the density of the output beams 2657 would increase. If abeam diameter of about 1 mm is assumed, it may be advantageous for thethickness of the eyepiece waveguide 2600 to be 325 μm or smaller so asto avoid an unacceptable degree of screen door effect. However,decreasing the thickness of the eyepiece waveguide 2600 can cause otherdifficulties, as shown in FIG. 26C.

FIG. 26C illustrates input coupling grating re-bounce, which is aneffect that can cause light to be disadvantageously lost from aneyepiece waveguide. FIG. 26C illustrates an eyepiece waveguide 2600 withan input coupling grating (ICG). An input beam 2602 is incident on theICG and is coupled into a guided propagation mode by the ICG. Theresulting guided beam 2656 then propagates through the eyepiecewaveguide 2600 via TIR. Depending on a variety of factors, including thesize of the ICG, the thickness of the eyepiece waveguide 2600, and thelight beam diameter, the guided beam 2656 may interact with the ICGafter having reflected from the opposite surface of the eyepiecewaveguide 2600. This situation is illustrated in FIG. 26C. The regionwhere this interaction occurs between the guided beam 2656 and the ICGis labeled as the re-bounce region.

In the re-bounce region, some of the power of the guided beam 2656 maybe out-coupled from the eyepiece waveguide 2600. For example, if theinput beam 2602 is coupled into the eyepiece waveguide 2600 by the +1diffractive order of the ICG, then the −1 diffractive order willout-couple the beam if it subsequently interacts with the ICG in there-bounce region. The ICG is typically designed with a high diffractiveefficiency in order to in-couple as much light as possible, but thathigh diffractive efficiency also results in strong out-coupling in there-bounce region. Thus, ICG re-bounce results in lost light and reducedefficiency.

The ICG re-bounce effect can be lessened by increasing the thickness ofthe eyepiece waveguide. As is evident from FIG. 26C, if the thickness ofthe eyepiece waveguide 2600 were larger, the guided beam 2656 wouldtravel a larger distance in the x-direction after diffracting from theICG and before returning to the surface of the eyepiece waveguide 2600that the ICG is located on. This would reduce the size of the re-bounceregion, or even eliminate it completely. If a beam diameter of about 1mm is assumed, it may be advantageous for the thickness of the eyepiecewaveguide 2600 to be 650 μm or larger so as to avoid ICG re-bounce.

As illustrated by FIGS. 26B and 26C, the thickness of the eyepiecewaveguide 2600 affects the severity of both the screen door effect andthe ICG re-bounce effect but in opposite ways. Decreasing the thicknessof the eyepiece waveguide 2600 lessens the screen door effect butworsens ICG re-bounce. Increasing the thickness of the eyepiecewaveguide 2600 lessens ICG re-bounce but worsens the screen door effect.Thus, in some embodiments, it would be advantageous to size thethickness of the eyepiece waveguide 2600 large enough to avoid ICGre-bounce while still limiting the screen door effect to an acceptabledegree. This can be accomplished by increasing the density of outputbeams 2657 that are supported by an eyepiece waveguide of a giventhickness. And this is precisely what is accomplished by thedouble-sided embodiment of the eyepiece waveguide 2600 that is shown inFIG. 26A.

FIG. 26D illustrates how the double-sided 2D CPE gratings in FIG. 26Aincrease the density of output beams from the eyepiece waveguide 2600.The top panel in FIG. 26D shows how the screen door effect is reducedfor the central portion of the FOV of the output image, while the bottompanel shows how the screen door effect is reduced for a peripheralportion of the FOV of the output image.

The top panel in FIG. 26D shows a guided beam 2656 propagating throughthe eyepiece waveguide 2600. In the top panel in FIG. 26D, guided beam2656 corresponds to a k-vector located at the center of the FOVrectangle for the image being displayed by the eyepiece waveguide 2600.A first 2D CPE grating 2655 a is provided on the top surface of theeyepiece waveguide, and a second 2D CPE grating 2655 b is provided onthe bottom surface. Output beams 2657 a result from interactions betweenguided beam 2656 and CPE grating 2655 a on the top surface of theeyepiece waveguide 2600, while output beams 2657 b result frominteractions between guided beam 2656 and CPE grating 2655 b on thebottom surface. Since the output beams 2655 a, 2655 b correspond to thecenter of the FOV of the output image, they exit the eyepiece waveguidenormal to its surface. As shown in FIG. 26D, output beams 2657 a and2657 b exit the eyepiece waveguide 2600 at alternating positions in thex-direction. Thus the density of output beams is increased.

The bottom panel in FIG. 26D also shows a guided beam 2656 propagatingthrough the eyepiece waveguide 2600. In the bottom panel in FIG. 26D,guided beam 2656 corresponds to a k-vector located at the periphery ofthe FOV rectangle for the image being displayed by the eyepiecewaveguide 2600. A first 2D CPE grating 2655 a is provided on the topsurface of the eyepiece waveguide, and a second 2D CPE grating 2655 b isprovided on the bottom surface. Output beams 2657 a result frominteractions between guided beam 2656 and CPE grating 2655 a on the topsurface of the eyepiece waveguide 2600, while output beams 2657 b resultfrom interactions between guided beam 2656 and CPE grating 2655 b on thebottom surface. Since the output beams 2655 a, 2655 b correspond to theperiphery of the FOV of the output image, they exit the eyepiecewaveguide at an angle. As shown in FIG. 26D, output beams 2657 a and2657 b exit the eyepiece waveguide 2600 at alternating positions in thex-direction. Thus the density of output beams is increased.

FIG. 26E illustrates the density of output beams 2657 for the eyepiecewaveguides shown in FIG. 24A (double-sided 1D CPE gratings), FIG. 25A(single-sided 2D CPE grating), and FIG. 26A (double-sided 2D CPEgratings). The solid lines represent light beams propagating via TIRfrom surface A (e.g., the eye-facing surface) of the eyepiece waveguideto surface B (e.g., the outward-facing surface), while the dashed linesrepresent light beams propagating from surface B to surface A. Eachpoint where a solid line turns to a dashed line, or vice versa,represents an interaction of a light beam with one of the surfaces of aneyepiece waveguide.

The left panel shows the density of output beams 2457 for thedouble-sided embodiment of FIG. 24A, which uses 1D CPE gratings 2455 a,2455 b. In that embodiment, the 1D CPE gratings 2455 a, 2455 b divide aguided beam 2441 into branches of spaced-apart diffracted beams 2456,but this occurs only with every other surface interaction. A part ofeach of those diffracted beams 2456 is then out-coupled as an outputbeam 2457 with every other surface interaction.

The middle panel shows the density of output beams 2557 for thesingle-sided embodiment of FIG. 25A, which uses a 2D CPE grating 2555 onone side of an eyepiece waveguide 2500. In that embodiment, the 2D CPEgrating 2555 divides a guided beam 2541 into branches of spaced-apartdiffracted beams 2556, and two branches are created with every othersurface interaction. A part of each of those diffracted beams 2556 isthen out-coupled as an output beam 2557 with every other surfaceinteraction.

The right panel shows the density of output beams 2657 for thedouble-sided embodiment of FIG. 26A, which uses 2D CPE gratings 2655 a,2655 b on both sides of an eyepiece waveguide 2600. In that embodiment,the CPE gratings 2655 a, 2655 b divide a guided input beam 2641 intobranches of spaced-apart diffracted beams 2656, and two branches arecreated with every surface interaction, rather than every other surfaceinteraction. In addition, a part of each of those diffracted beams 2656is then out-coupled as an output beam 2557 with every surfaceinteraction, rather than every other surface interaction. Thedouble-sided embodiment of FIG. 26A therefore doubles the density ofoutput beams 2557 in the x-direction and in the y-direction. Thisresults in a 4× increase in the density of output beams 2557 per unitarea when compared with the single-sided design in FIG. 25A.

Due to the increased density of output beams 2557 from the double-sidedeyepiece waveguide 2600 with 2D CPE gratings 2655 a, 2655 b, this designcan be used to limit the severity of the screen door effect while stillallowing for the eyepiece waveguide 2600 to be thick enough to reduce oreliminate ICG re-bounce. For example, in some embodiments, the eyepiecewaveguide 2600 may be as thick as approximately one third (e.g., ±10%,or ±20%, or ±30%) of the diameter of the input beams of light.

FIG. 26F shows example simulated images produced by eyepiece waveguideswith 2D CPE gratings; images for both the case of the single-sidedembodiment of FIG. 25A and the double-sided embodiment of FIG. 26A areshown. Images i) and ii) were produced by the single-sided embodiment ofFIG. 25A. Image i) was created using an LED light source (with aspectrum of about 20 nm), whereas image ii) was created using a laserlight source (with a spectrum of about 2 nm). The LED image has betteruniformity than the laser image—due to a smearing effect from thebroader bandwidth of the LED—but high-frequency screen door artifact ispresent in both images.

Images iii) and iv) were produced by the double-sided embodiment of FIG.26A. Image iii) was created using the LED light source, while image iv)was created using the laser light source. There is a clear reduction inhigh-frequency screen door artifact in the images produced by thedouble-sided embodiment of FIG. 26A. This reduction in screen doorartifact is attributable to the increased density of output beams forthe double-sided embodiment.

Additional Considerations

Any of the features described herein with respect to any eyepiecewaveguide can alternatively be implemented with any other eyepiecewaveguide described herein.

Unless the context clearly requires otherwise, throughout thedescription and the claims, the words “comprise,” “comprising,”“include,” “including,” “have” and “having” and the like are to beconstrued in an inclusive sense, as opposed to an exclusive orexhaustive sense; that is to say, in the sense of “including, but notlimited to.” The word “coupled”, as generally used herein, refers to twoor more elements that may be either directly connected, or connected byway of one or more intermediate elements. Likewise, the word“connected”, as generally used herein, refers to two or more elementsthat may be either directly connected, or connected by way of one ormore intermediate elements. Depending on the context, “coupled” or“connected” may refer to an optical coupling or optical connection suchthat light is coupled or connected from one optical element to anotheroptical element. Additionally, the words “herein,” “above,” “below,”“infra,” “supra,” and words of similar import, when used in thisapplication, shall refer to this application as a whole and not to anyparticular portions of this application. Where the context permits,words in the above Detailed Description using the singular or pluralnumber may also include the plural or singular number, respectively. Theword “or” in reference to a list of two or more items is an inclusive(rather than an exclusive) “or”, and “or” covers all of the followinginterpretations of the word: any of the items in the list, all of theitems in the list, and any combination of one or more of the items inthe list, and does not exclude other items being added to the list. Inaddition, the articles “a,” “an,” and “the” as used in this applicationand the appended claims are to be construed to mean “one or more” or “atleast one” unless specified otherwise.

As used herein, a phrase referring to “at least one of” a list of itemsrefers to any combination of those items, including single members. Asan example, “at least one of: A, B, or C” is intended to cover: A, B, C,A and B, A and C, B and C, and A, B, and C. Conjunctive language such asthe phrase “at least one of X, Y and Z,” unless specifically statedotherwise, is otherwise understood with the context as used in generalto convey that an item, term, etc. may be at least one of X, Y or Z.Thus, such conjunctive language is not generally intended to imply thatcertain embodiments require at least one of X, at least one of Y and atleast one of Z to each be present.

Moreover, conditional language used herein, such as, among others,“can,” “could,” “might,” “may,” “e.g.,” “for example,” “such as” and thelike, unless specifically stated otherwise, or otherwise understoodwithin the context as used, is generally intended to convey that certainembodiments include, while other embodiments do not include, certainfeatures, elements and/or states. Thus, such conditional language is notgenerally intended to imply that features, elements, and/or states arein any way required for one or more embodiments or whether thesefeatures, elements, and/or states are included or are to be performed inany particular embodiment.

While certain embodiments have been described, these embodiments havebeen presented by way of example only, and are not intended to limit thescope of the disclosure. Features of any one of the embodiments can becombined and/or substituted with features of any other one of theembodiments. Certain advantages of various embodiments have beendescribed herein. But not all embodiments necessarily achieve each ofthese advantages.

Embodiments have been described in connection with the accompanyingdrawings. However, the figures are not drawn to scale. Distances,angles, etc. are merely illustrative and do not necessarily bear anexact relationship to actual dimensions and layout of the devicesillustrated.

The foregoing embodiments have been described at a level of detail toallow one of ordinary skill in the art to make and use the devices,systems, methods, etc. described herein. A wide variety of variation ispossible. Components, elements, and/or steps may be altered, added,removed, or rearranged. While certain embodiments have been explicitlydescribed, other embodiments will become apparent to those of ordinaryskill in the art based on this disclosure.

What is claimed is:
 1. An eyepiece waveguide for an augmented realitydisplay system, the eyepiece waveguide comprising: an opticallytransmissive substrate having a first surface and a second surface; aninput coupling grating (ICG) region formed on or in one of the surfacesof the substrate, the ICG region being configured to receive an inputbeam of light and to couple the input beam into the substrate as aguided beam; a first combined pupil expander-extractor (CPE) gratingregion formed on or in the first surface of the substrate, the first CPEgrating region being positioned to receive the guided beam from the ICGregion and to create a first plurality of diffracted beams at aplurality of distributed locations, and to out-couple a first pluralityof output beams; and a second CPE grating region formed on or in thesecond surface of the substrate, the second CPE grating region beingpositioned to receive the guided beam from the ICG region and to createa second plurality of diffracted beams at a plurality of distributedlocations, and to out-couple a second plurality of output beams.
 2. Theeyepiece waveguide of claim 1, wherein the first CPE grating region isconfigured to out-couple the second plurality of diffracted beams, andthe second CPE grating region is configured to out-couple the firstplurality of diffracted beams.
 3. The eyepiece waveguide of claim 2,wherein the first and second plurality of diffracted beams alternatelyinteract with the first and second CPE grating regions.
 4. The eyepiecewaveguide of claim 1, wherein the first CPE grating region and thesecond CPE grating region both comprise a plurality of periodicallyrepeating diffractive lines, and wherein the diffractive lines of thefirst CPE grating region are oriented at an angle of substantially 60°with respect to the diffractive lines of the second CPE grating region.5. The eyepiece waveguide of claim 4, wherein the diffractive lines ofthe first and second CPE grating regions have the same period.
 6. Theeyepiece waveguide of claim 4, wherein the diffractive lines of thefirst and second CPE grating regions are formed using a common mastertemplate.
 7. The eyepiece waveguide of claim 4, wherein the ICG regioncomprises a plurality of periodically repeating diffractive lines, andwherein the diffractive lines of the ICG region are oriented at an angleof substantially 60° with respect to the diffractive lines of the firstCPE grating region and the diffractive lines of the second CPE gratingregion.
 8. The eyepiece waveguide of claim 7, wherein the diffractivelines of the ICG region, the first CPE grating region, and the secondCPE grating region have the same period.
 9. The eyepiece waveguide ofclaim 1, wherein the first and second CPE grating regions overlap by atleast 90%.
 10. The eyepiece waveguide of claim 1, wherein the first andsecond CPE grating regions are the same size.
 11. The eyepiece waveguideof claim 10, wherein the first and second CPE grating regions arealigned with one another.
 12. The eyepiece waveguide of claim 1, whereinthe first CPE grating region is configured to create the first pluralityof diffracted beams by diffracting portions of the power of the guidedbeam from the ICG region in at least two directions.
 13. The eyepiecewaveguide of claim 12, wherein one of the two directions corresponds toa zero order diffracted beam.
 14. The eyepiece waveguide of claim 1,wherein the second CPE grating region is configured to create the secondplurality of diffracted beams by diffracting portions of the power ofthe guided beam from the ICG region in at least two directions.
 15. Theeyepiece waveguide of claim 14, wherein one of the two directionscorresponds to a zero order diffracted beam.
 16. The eyepiece waveguideof claim 1, wherein the first plurality of diffracted beams propagate ina first direction, and wherein the second plurality of diffracted beamspropagate in a second direction at an angle of substantially 60° withrespect to the first direction.
 17. The eyepiece waveguide of claim 1,wherein the input beam is collimated and has a diameter of 5 mm or less.18. The eyepiece waveguide of claim 1, wherein the opticallytransmissive substrate is planar.
 19. The eyepiece waveguide of claim 1,wherein the eyepiece waveguide is incorporated into an eyepiece for anaugmented reality display system.
 20. The eyepiece waveguide of claim19, wherein the eyepiece is configured to display color images at aplurality of depth planes.
 21. The eyepiece waveguide of claim 1,wherein the ICG region is configured receive a set of a plurality ofinput beams of light, the set of input beams being associated with a setof k-vectors which form a field of view (FOV) shape located at thecenter of a k-space annulus associated with the eyepiece waveguide;wherein the ICG region is configured to diffract the input beams so asto couple them into the substrate as guided beams and so as to translatethe FOV shape to a first position at least partially within the k-spaceannulus; wherein the first CPE grating region is configured to diffractthe guided beams so as to translate the FOV shape to a second positionat least partially within the k-space annulus; and wherein the secondCPE grating region is configured to diffract the guided beams so as totranslate the FOV shape to a third position at least partially withinthe k-space annulus.
 22. The eyepiece waveguide of claim 21, wherein thecenter of the k-space annulus, the first position, and the secondposition define a first equilateral triangle in k-space.
 23. Theeyepiece waveguide of claim 22, wherein the center of the k-spaceannulus, the first position, and the third position define a secondequilateral triangle in k-space.
 24. The eyepiece waveguide of claim 23,wherein the first and second equilateral triangles in k-space share aside.
 25. An eyepiece waveguide for an augmented reality display system,the eyepiece waveguide comprising: an optically transmissive substrate;an input coupling grating (ICG) region; a first combined pupilexpander-extractor (CPE) grating region; and a second CPE gratingregion, wherein the ICG region is configured receive a set of aplurality of input beams of light, the set of input beams beingassociated with a set of k-vectors which form a field of view (FOV)shape located at the center of a k-space annulus associated with theeyepiece waveguide, wherein the ICG region is configured to diffract theinput beams so as to couple them into the substrate as guided beams andso as to translate the FOV shape to a first position at least partiallywithin the k-space annulus, wherein the first CPE grating region isconfigured to diffract the guided beams so as to translate the FOV shapefrom the first position to a second position at least partially withinthe k-space annulus, wherein the second CPE grating region is configuredto diffract the guided beams so as to translate the FOV shape from thefirst position to a third position at least partially within the k-spaceannulus, wherein the first CPE grating region is configured to diffractthe guided beams so as to translate the FOV shape from the thirdposition to the center of the k-space annulus, and wherein the secondCPE grating region is configured to diffract the guided beams so as totranslate the FOV shape from the second position to the center of thek-space annulus.
 26. The eyepiece waveguide of claim 25, wherein thecenter of the k-space annulus, the first position, and the secondposition define a first equilateral triangle in k-space.
 27. Theeyepiece waveguide of claim 26, wherein the center of the k-spaceannulus, the first position, and the third position define a secondequilateral triangle in k-space.
 28. The eyepiece waveguide of claim 27,wherein the first and second equilateral triangles in k-space share aside.
 29. The eyepiece waveguide of claim 25, wherein the first CPEgrating region and the second CPE grating region are formed on or inopposing sides of the optically transmissive substrate.
 30. The eyepiecewaveguide of claim 25, wherein the guided beams alternately interactwith the first and second CPE grating regions.
 31. The eyepiecewaveguide of claim 25, wherein a first-order grating vector associatedwith the first CPE grating region has the same magnitude as afirst-order grating vector associated with the second CPE gratingregion.
 32. The eyepiece waveguide of claim 31, wherein a first-ordergrating vector associated with the ICG region has the same magnitude asthe first-order grating vector associated with the first CPE gratingregion and the first-order grating vector associated with the second CPEgrating region.
 33. The eyepiece waveguide of claim 25, wherein theeyepiece waveguide is incorporated into an eyepiece for an augmentedreality display system.
 34. The eyepiece waveguide of claim 33, whereinthe eyepiece is configured to display color images at a plurality ofdepth planes.
 35. An eyepiece waveguide for an augmented reality displaysystem, the eyepiece waveguide comprising: an optically transmissivesubstrate having a first surface and a second surface; an input couplinggrating (ICG) region formed on or in one of the surfaces of thesubstrate, the ICG region being configured to receive a beam of lightand to couple the beam into the substrate in a guided propagation mode;and a first combined pupil expander-extractor (CPE) grating regionformed on or in the first surface of the substrate, the first CPEgrating region being positioned to receive the beam of light from theICG region, and the first CPE grating region comprising a plurality ofdiffractive features configured to alter the propagation direction ofthe beam with a first interaction, and to out-couple the beam from theeyepiece waveguide with a second interaction.
 36. The eyepiece waveguideof claim 35, wherein the plurality of diffractive features of the firstCPE grating region exhibit periodicities in at least two directions. 37.The eyepiece waveguide of claim 36, wherein the plurality of diffractivefeatures of the first CPE grating region exhibit periodicities in firstand second directions oriented at an angle of substantially 60° withrespect to one another.
 38. The eyepiece waveguide of claim 37, whereinthe ICG region comprises a plurality of diffractive features thatexhibit periodicity in a third direction oriented at an angle ofsubstantially 60° with respect to both the first direction and thesecond direction.
 39. The eyepiece waveguide of claim 35, furthercomprising a second CPE grating region formed on or in the secondsurface of the substrate, the second CPE grating region comprising aplurality of diffractive features configured to alter the propagationdirection of the beam with a first interaction, and to out-couple thebeam from the eyepiece waveguide with a second interaction.
 40. Theeyepiece waveguide of claim 39, wherein the first and second CPE gratingregions are identical.
 41. The eyepiece waveguide of claim 39, whereinthe substrate has a thickness that is large enough to prevent the beamfrom interacting with the ICG region after having been coupled into theguided propagation mode.
 42. The eyepiece waveguide of claim 35, whereinthe beam is collimated and has a diameter of 5 mm or less.
 43. Theeyepiece waveguide of claim 35, wherein the optically transmissivesubstrate is planar.
 44. The eyepiece waveguide of claim 35, wherein theeyepiece waveguide is incorporated into an eyepiece for an augmentedreality display system.
 45. The eyepiece waveguide of claim 44, whereinthe eyepiece is configured to display color images at a plurality ofdepth planes.
 46. An eyepiece waveguide for an augmented reality displaysystem, the eyepiece waveguide comprising: an optically transmissivesubstrate; an input coupling grating (ICG) region; and a first combinedpupil expander-extractor (CPE) grating region formed on a first side ofthe substrate, wherein the ICG region is configured to receive a set ofa plurality of input beams of light, the set of input beams beingassociated with a set of k-vectors which form a field of view (FOV)shape located at the center of a k-space annulus associated with theeyepiece waveguide, wherein the ICG region is configured to diffract theinput beams so as to couple them into the substrate as guided beams andso as to translate the FOV shape to a first position at least partiallywithin the k-space annulus, wherein, with a first interaction, the firstCPE grating region is configured to diffract the guided beams so as totranslate the FOV shape from the first position to second and thirdpositions at least partially within the k-space annulus, and wherein,with a second interaction, the first CPE grating region is configured todiffract the guided beams so as to translate the FOV shape from thesecond and third positions to the center of the k-space annulus.
 47. Theeyepiece waveguide of claim 46, wherein the center of the k-spaceannulus, the first position, and the second position define a firstequilateral triangle in k-space.
 48. The eyepiece waveguide of claim 47,wherein the center of the k-space annulus, the first position, and thethird position define a second equilateral triangle in k-space.
 49. Theeyepiece waveguide of claim 48, wherein the first and second equilateraltriangles in k-space share a side.
 50. The eyepiece waveguide of claim46, further comprising a second CPE grating region formed on a secondside of the substrate, wherein, with a first interaction, the second CPEgrating region is configured to diffract the guided beams so as totranslate the FOV shape from the first position to the second and thirdpositions at least partially within the k-space annulus; and wherein,with a second interaction, the second CPE grating region is configuredto diffract the guided beams so as to translate the FOV shape from thesecond and third positions to the center of the k-space annulus.
 51. Theeyepiece waveguide of claim 50, wherein the second CPE grating regionincreases the density of output beams from the eyepiece waveguide. 52.The eyepiece waveguide of claim 51, wherein the second CPE gratingregion increases the density of output beams by at least a factor offour.